Abstract
In Chapters Two to Five we devote our attentions primarily to issues regarding parameter-sensitivity analysis. In spite of different uncertainties which may exist in a dynamical system, we expect that our controller will ultimately maintain qualitatively and/or quantitatively the overall system operation as desired. Or it will maintain this operation within a prespecified class of such operations which this is really the key issue in any robustness methodology. Therefore we must incorporate in control synthesis algorithm any information regarding possible discrepancies in system “output”, in order to generate new controllers that can stand against the consequences of some possible uncertainties. This incorporation is by no means a simple task, and before we let our expectations exceed our means, we examine some of our earlier assumptions and review the class of problems which currently can be analyzed.
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References
[A] Trajectory — Sensitivity Comparison Certain Feedback Properties of Linear Systems
B.D.O. Anderson, “Sensitivity improvement using optimal design,” Proc. IEE, vol. 113, pp. 1084–1086, 1966.
D. Bensoussan, “Sensitivity reduction in single-input single-output systems,” IJC, vol. 39, no. 2, pp. 321–335, 1984.
D. Bensoussan, “Decentralized control and sensitivity reduction of weakly coupled plants,” IJC, vol. 40, no. 6, pp. 1099–1118, 1984.
R.W. Brockett and M.D. Mesarovic, “The reproducibility of multivariable systems,” JMAA, vol. 11, pp. 548–563, 1965.
B.M. Chen, A. Saberi, and P. Sannuti, “A new stable compensator design for exact and approximate loop transfer recovery,” Automatica, vol. 27, no. 2, pp. 257–280, 1991.
B.M. Chen, A. Saberi, and P. Sannuti, “Necessary and sufficient conditions for a nonminimum phase plant to have a recoverable target loop — A stable compensator design for LTR,” Automatica, vol. 28, no. 3, pp. 493–507, 1992.
J.B. Cruz, Jr., and W.R. Perkins, “A new approach to the sensitivity problem in multivariable feedback system design,” IEEE-TAC, vol. AC-9, pp. 216–223, July 1964.
J.B. Cruz, Jr., and W.R. Perkins, “Criteria for system sensitivity to parameter variations,” Proc. IFAC, vol. 1 (of the 3rd Congress), pp. 18C. 1–18C. 7, 1966.
J.B. Cruz, Jr., and N. Sundararajan, “Sensitivity improvement of semi-closed loop systems,” in Proc. 2nd IFAC Symp. Multivariable Technical Control Systems, pp. 1–15, 1971.
R.M. DeSantis and S. Lefebvre, “Comparative sensitivity and absolute invariant compensators,” in Proc. Allerton Conf., pp. 964–973, 1976.
R.M. DeSantis and W.A. Porter, “Circle type conditions for sensitivity reduction,” ACTA, vol. 2, no. 2, pp. 26–36, May 1974.
C.A. Desoer and W.S. Chan, “The feedback interconnection of lumped linear time-invariant systems,” JFI, vol. 300, nos. 5 amp 6, pp. 335–351, 1975.
M. Eslami, “On sensitivity comparison of linear systems,” in Proc. MECO’ 77 (M.H. Hamza, Ed.), pp. 119–123, Zurich, June 20–21, 1977.
R.L. Gonzales, “Synthesis for minimum sensitivity under worst case conditions,” in Proc. Allerton Conf., pp. 527–537, 1966.
O.R. Gonzalez and P.J. Antsaklis, “Sensitivity considerations in the control of generalized plants,” IEEE-TAC, vol. AC-34, no. 8, pp. 885–889, Aug. 1989.
G. Grubel and G. Kreisselmeier, “A generalized comparison sensitivity concept for sensitivity reduction in control system design,” in Proc. Joint Auto. Contr. Conf., pp. 328–332, 1974.
Y. Hontoir and J.B. Cruz, Jr., “Sensitivity reduction in linear systems,” Automatica, vol. 8, pp. 445–449, 1972.
Y. Hontoir and J.B. Cruz, “A probabilistic likelihood approach to trajectory sensitivity,” Automatica, vol. 10, pp. 49–60, 1974.
W.F. Horton and C.T. Leondes, “Sensitivity in multivariable control systems,” ASME-JBE, pp. 246–250, June 1969.
O.L.R. Jacobs, “Cost of uncertainty about controlled objects,” Proc. IEE, vol. 136, Pt. D, no. 4, pp. 177–187, July 1989.
A.V. Knyazev, “Frozen-parameter method for integral equations of feedback system dynamics,” ARC, vol. 41, no. 10, pp. 1347–1348, Oct. 1980.
E. Kreindler, “On the definition and application of the sensitivity function,” JFI, vol. 285, pp. 26–36, Jan. 1968.
E. Kreindler, “Closed-loop sensitivity reduction of linear optimal control systems,” IEEE-TAC, vol. AC-13, no. 3, pp. 254–262, June 1968.
E. Kreindler, “On trajectory sensitivity in optimal control,” Proc. IEEE, vol. 57, no. 4, pp. 695–696, April 1969.
G. Kreisselmeier and G. Grubel, “The design of optimally parameter insensitive control systems,” in Proc. IFAC, vol. 3 (of the 5th Congress), pp. 31.1.1–31.1. 6, 1972.
B. Krogh and J.B. Cruz, Jr., “Design of sensitivity-reducing compensators using observers,” IEEE-TAC, vol. AC-23, no. 6, pp. 1058–1062, Dec. 1978. Addendum, ibid., vol. AC-24, no. 2, p. 353, April 1979.
D.F. Looze and J.S. Freudenberg, “Limitations of feedback properties imposed by open-loop right half plane poles,” IEEE-TAC, vol. AC-36, no. 6, pp. 736–739, 1991.
A.GJ. MacFarlane, “Return-difference and return-ratio matrices and their use in analysis and design of multivariable feedback control systems,” Proc. IEE, vol. 117, no. 10, pp. 20372049, Oct. 1970.
A.GJ. MacFarlane, “Return-difference and return-ratio matrices and their use in analysis and design of multivariable feedback control systems,” Proc. IEE, vol. 118, no. 7, pp. 946–947, July 1971.
P.J. Marino, “On the synthesis of insensitive linear feedback control systems,” IJC, vol. 6, no. 1, pp. 33–50, 1967.
W.R. Perkins and J.B. Cruz, Jr., “The parameter variation problem in state feedback control systems,” ASME-JBE, vol. 87, pp. 120–124, 1965.
A.GJ. MacFarlane, “Feedback properties of linear regulators,” IEEE-TAC, vol. AC-16, no$16, pp. 659–663, Dec. 1971.
W.R. Perkins, J.B. Cruz, Jr., and R.L. Gonzales, “Design of minimum sensitivity systems,” IEEE-TAC, vol. AC-13, no. 2, pp. 159–167, April 1968.
H.J. Perlis, “On the residue of a sensitivity function,” IEEE-TAC, vol. AC-10, pp. 496–497, Oct. 1965.
W.A. Porter, “A design technique for improving system sensitivity,” in Proc. Alterton Conf., pp. 517–526, 1966.
W.A. Porter, “On the reduction of sensitivity in multivariate systems,” IJC, vol. 5, no. 1, pp. 1–9, 1967.
V.R. Suie and V.V. Athani, “Directional sensitivity tradeoffs in multivariable feedback systems,” Automatica, vol. 27, no. 5, pp. 869–872, 1991.
N. Sundararajan and J.B. Cruz, Jr., “Trajectory insensitivity of optimal feedback systems,” IEEE-TAC, vol. AC-15, pp. 663–665, Dec. 1970.
C. Verde and P.M. Frank, “Sensitivity reduction of linear quadratic regulator by matrix modification,” IJC, vol. 48, no. 1, pp. 211–223, 1988.
[B] Performance - Index Sensitivity Comparison
P. Courtin and J. Rootenberg, “Performance index sensitivity of optimal control systems,” IEEE-TAC, vol. AC-16, no. 3, pp. 275–277, June 1971.
P. Dorato, “On sensitivity in optimal control systems,” IEEE-TAC, vol. AC-8, pp. 256–257, July 1963.
J.C. Dunn, “Further results on the sensitivity of optimally controlled systems,” IEEE-TAC, vol. AC-12, pp. 324–326, June 1967.
H.S. Kang and A.K. Mahalanabis, “Sensitivity of the performance of optimal stochastic systems,” Proc. IEEE, vol. 61, no. 3, pp. 389–390, 1973.
P.V. Kokotovic, J. Heller, and P. Sannuti, “Sensitivity comparison of optimal controls,” IJC, vol. 9, no. 1, pp. 111–115, Jan. 1969.
E. Kreindler, “On performance sensitivity of optimal control systems,” IJC, vol. 15, no. 3, pp. 481–486, 1972.
A. Orbach and R. Fischl, “Performance index sensitivity of optimal control of first order in time-and space-distributed parameter systems,” IEEE-TAC, voL AC-25, no. 2, pp. 314–317, April 1980.
B. Pagurek, “Sensitivity of the performance of optimal linear control systems to parameter variations,” IJC, vol. 1, pp. 33–45, 1965.
B. Pagurek, “Sensitivity of the performance of optimal control systems to plant parameter vari- ations,” IEEE-TAC, AC-10, pp. 178–180, April 1965.
W.A. Porter, “Sensitivity problems in linear systems,” IEEE-TAC, vol. AC-10, July 1965.
N.K. Sinha and S.R. Atluri, “Sensitivity of optimal control systems,” in Proc. Allerton Conf., pp. 508–516, 1966.
N.K. Sinha, S.R. Atluri, and H.S. Witsenhausen, “On the sensitivity of optimal control systems with quadratic performance criteria,” IEEE-TAC, vol. AC-12, pp. 208–209, April 1967.
F.E. Thau, “A Comparison of closed-loop and open-loop optimum systems,” IEEE-TAC, vol. AC-11, pp. 619–620, July 1966.
H.S. Witsenhausen, “On the sensitivity of optimal control systems,” IEEE-TAC, vol. AC-10, pp. 495–496, Oct. 1965.
D.C. Youla and P. Dorato, “On the comparison of the sensitivities of open-loop and closed-loop optimal control systems,” IEEE-TAC, vol. AC-13, pp. 186–188, April 1968.
[C] Optimality - Index Sensitivity: Analysis and Synthesis
Y.V. Aleksandrov, “Sensitivity of the quality criterion of linear optimal systems,” ECy, vol. 9, no. 5, pp. 948–953, Sept./Oct. 1971.
Y.V. Aleksandrov, “Guaranteed sensitivity of linear optimal systems,” ECy, vol. 13, no. 2, pp. 140–145, March/April 1975.
M. Aoki, “On performance losses in some adaptive control systems: I, ASME-JBE, pp. 9094, March 1965.
N. Becker, “A note on performance index sensitivity of time optimal control systems,” IEEE-TAC, vol. AC-25, no. 4, pp. 819–821, Aug. 1980.
D.S. Bernstein and W.M. Haddad, “Robust stability and performance analysis for linear dynamic systems,” IEEE-TAC, vol. AC-34, no. 7, pp. 751–758, July 1989.
B.Z. Bobrovsky and D. Graupe, “Analysis of optimal-cost sensitivity to parameter changes,” IEEE-TAC,vol. AC-16, pp. 487–488, Oct. 1971.
W.A. Brown and W.J. Vetter, “Sub-optimal design of the linear regulator with incomplete state feedback via second-order sensitivity,” IJC, vol. 16, no. 1, pp. 1–7, 1972.
RJ. Bums and K.S.P. Kumar, “Sensitivity considerations in specific optimum controls,” IJC, vol. 5, no. 3, pp. 289–296, 1967.
B.N. Chatterji, “Sensitivity of performance of control systems to unintentional coupling signals,” IJC, vol. 12, no. 2, pp. 265–272, 1970.
M. Eslami, “Sensitivity analysis and synthesis in automatic control systems,” Ph.D. Dissertation, The University of Wisconsin - Madison, May 1978.
M. Goujon and M. Lecrique, “Influence de la precision des regulateurs sur les performances des systemes de reglage,” Automatisme, vol. XVI, no. 2, pp. 100–110, Feb. 1971.
D. Graupe, “Optimal linear control subject to sensitivity constraints,” IEEE-TAC, vol. AC-19, no. 5, pp. 593–594, Oct. 1974.
A.J. Koivo, “Performance Sensitivity of dynamic systems,” in Proc. Joint Auto. Contr. Conf., pp. 444–453, 1968.
], “Performance sensitivity of dynamical systems,” Proc. IEE, vol. 117, no. 4, pp. 825–830, April 1970.
B. Kurtaran and M. Sidar, “Analysis of cost sensitivity for linear-quadratic stochastic problems with instantaneous output feedback,” IEEE-TAC, vol. AC-19, no. 5, pp. 589–590, Oct. 1974.
W.S. Levine and M. Athans, “On the determination of the optimal constant output feedback gain for linear multivariable systems,” IEEE-TAC, vol. AC-15, pp. 44–48, Feb. 1970.
E.P. Maslov and A.M. Petrovsky, “Sensitivity of linear systems with respect to random disturbances,” Automatica, vol. 5, pp. 275–278, 1969.
N.H. McClamroch, L.G. Clark, and J.K. Aggarwal, “Sensitivity of linear control systems to large parameter variations,” Automatica, vol. 5, pp. 257–263, 1969.
J. Medanic, “Three segment method in the sensitivity design of control systems,” in Proc. Allerton Conf., pp. 439–450, 1967.
M. Midy, “Influence d’une non-linearite sur les parametres de reglage d’une boucle de regulation analogique (application a une regulation de debit),” Automatisme, vol. XVI, no. 2, pp. 116–121, Feb. 1971.
L. Platzman and M. Athans, “Explicit cost sensitivity analysis for linear systems with quadratic criteria,” IEEE-TAC, vol. AC-20, no. 2, pp. 252–254, April 1975.
J.J. Rissanen, “Performance deterioration of optimum systems,” IEEE-TAC, vol. AC-11, pp. 530–532, July 1966.
R.A. Rohrer and M. Sobral, Jr., “Sensitivity considerations in optimal system design,” IEEE-TAC, vol. AC-10, pp. 43–48, Jan. 1965.
Y.E. Sagalov, “Analysis of sensitivity of an optimal system with parameter variation,” ARC, no. 2, pp. 180–184, Feb. 1974.
M.P. Sakharov, “Parametric sensitivity in the problem of control with an incomplete plant model,” ARC, no. 6, pp. 877–883, June 1973.
D.M. Salmon, “Minimax controller design,” IEEE-TAC, vol. AC-13, no. 4, pp. 369–376, Aug. 1968.
N.K. Sinha and S.H. Dai, “Reduction of the sensitivity of an optimal control system to plant parameter variations,” IEEE-TAC, vol. AC-15, pp. 589–590, Oct. 1970.
J.S. Tyler, Jr., and F.B. Tuteur, “The use of a quadratic performance index to design multivariable control systems,” IEEE-TAC, vol. AC-11, no. 1, pp. 84–92, Jan. 1966.
A.A. Vengerov, V.L. Rozhanskii, and G.M. Ulanov, “Estimation of sensitivity of integral performance criteria of systems of variable structure,” ARC, no. 2, pp. 245–250, Feb. 1971.
R.A. Werner, “Feedback control with magnitude constraints for systems with unknown parameters,” in Proc. Allerton Conf, pp. 418–427, 1967.
R.A. Werner and J.B. Cruz, Jr., “Feedback control which preserves optimality for systems with unknown parameters,” IEEE-TAC, vol. AC-13, no. 6, pp. 621–629, Dec. 1968.
M.A. Zohdy and J.D. Aplevich, “Output feedback controllers optimal for time-multiplied performance indices,” Elect. Lett., vol. 11, no. 16, pp. 360–361, Aug. 1975.
[D] Trajectory — Sensitivity Optimization
M.A. Abouelwafa and M.H. Hamza, “Design of an adaptive controller using multi-level and sensitivity concepts,” IJSS, vol. 10, no. 3, pp. 243–250, 1979.
A.J. Bradt, “Sensitivity functions in the design of optimal controllers,” IEEE-TAC, voL AC-13, pp. 110–111, Feb. 1968.
P.C. Byrne and M. Burke, “Optimization with trajectory sensitivity considerations,” IEEE-TAC, vol. AC-21, no. 2, pp. 282–283, April 1976. Comments, by P.J. Fleming and M.M. Newmann, ibid., vol. AC-22, no. 1, p. 151, Feb. 1977.
J.F. Cassidy, Jr., and I. Lee, “On the optimal feedback control of a large launch vehicle to reduce trajectory sensitivity,” in Proc. Joint Auto. Contr. Conf, pp. 587–595, June 1967.
V.V. Ciric and J.V. Leeds, “Further results on sensitivity consideration of multiple-input controller design for dynamic optimization,” IJC, vol. 15, no. 5, pp. 849–863, 1972.
RN. Crane and A.R. Stubberud, “Minimum sensitive linear feedback compensators,” in Proc. Asilomar Conf, pp. 405–409, 1971.
RN. Crane and A.R. Stubberud, “Closed-loop formulations of optimal control problems for minimum sensitivity,” in Control and Dynamic Systems advances in theory and applications, vol. 9 (C.T. Leondes, Ed.). New York: Academic Press, pp. 375–505, 1973.
H. D’Angelo, M.L. Moe, and T.C. Hendricks, “Trajectory sensitivity of an optimal control system,” in Proc. Allerton Conf., pp. 489–498, Oct. 1966.
H.J. Dougherty, I. Lee, and P.M. DeRusso, “Synthesis of optimal feedback control systems subject to parameter variations,” preprints of Joint Auto. Contr. Conf., pp. 125–133, 1967.
M. Eslami, “Sensitivity analysis and synthesis in automatic control systems,” Ph.D. Dissertation, The University of Wisconsin — Madison, May 1978.
M. Eslami, “On sensitivity measure optimization with large parameter variation,” The Univer- sity of Wisconsin-Madison, Dept. of ECE, Report ECE-79–3, 32 pp., Jan. 1979.
M. Eslami, “On sensitivity minimization algorithms with quadratic performances,” in Proc. 21st IEEE Conf. on Decision and Contr., pp. 637–641, Dec. 1982.
M. Eslami, “Robust quadratic optimization of systems with large parameter variations,” JOCAM, voL 12, no. 1, pp. 33–48, 1991. Corrections, ibid., vol. 15, 1994.
M. Eslami and R.S. Marleau, “On sensitivity minimization with an adaptive controller,” in Proc. Joint Auto. Contr. Conf., pp. 219–228, Oct. 1978.
M. Eslami and R.S. Marleau, “On trajectory sensitivity minimization with an adaptive controller,” in Advances in Control (D.G. Lainiotis and T.S. Tzannes, Eds.). Boston: D. Reidel Pub. Company, pp. 342–350, 1980.
P.J. Fleming and M.M. Newmann, “Trajectory sensitivity reduction in the optimal linear regulator,” in Recent Mathematical Development in Control (DJ. Bell, Ed.). New York: Academic Press, pp. 137–151, 1973.
P.J. Fleming and M.M. Newmann, “Design algorithms for a sensitivity constrained suboptimal regulator,” IJC, vol 25, no. 6, pp. 965–978, 1977.
I.-K. Fong, T.-S. Kuo, K.-C. Kuo, C.-F. Hsu, and M.-Y. Wu, “Sensitivity analysis of linear uncertain systems and its application in the synthesis of an insensitive linear regulator,” IJSS, vol. 18, no. 1, pp. 43–55, 1987.
G. Fronza and A. Locatelli, “Insensitivity by linear feedback,” JFI, vol. 296, no. 4, pp. 237247, Oct. 1973.
S. Fu, M.E. Sawan, Y. Fu, and M.T. Tran, “Trajectory sensitivity analysis: A new criterion,” IJSS, vol. 16, no. 6, pp. 769–775, 1985.
M. Gopal and P. Pratapachandran Nair, “Sensitivity reduced optimal linear regulator with prescribed closed-loop eigenvalues,” IEEE-TAC, vol. AC-29, no. 7, pp. 661–664, July 1984.
M. Gopal and P. Pratapachandran Nair, “On the design of a sensitivity-reducing optimal dead-beat controller,” IJC, vol. 42, no. 4, pp. 877–886, 1985.
G. Grubel and G. Kreisselmeier, “Effective parameter sensitivity reduction through minimization of sensitivity measure,” in Proc. Joint Auto. Contr., pp. 79–86, 1971.
R.P. Hamalainen and T. Eirola, “Trajectory sensitivity reduction in non-zero-sum differential games,” IJSS, vol. 11, no. 2, pp. 207–222, 1980.
A.R. Hanafy, “Two-level optimization technique to minimize trajectory sensitivity,” in Proc. Joint Auto. Contr. Conf., pp. 568–575, 1976.
E. Higginbotham, “Optimal sensitivity and state control of regulators containing plant and measurement noise,” in Proc. Allerton Conf., pp. 677–680, 1969.
Y. Hontoir and J.B. Cruz, Jr., “Minimum trajectory sensitivity design of systems with random parameters,” IJC, vol. 20, no. 3, pp. 353–362, 1974.
S.J. Kahne, “Low sensitivity design of optimal linear control systems,” IEEE-TAES, vol. AES-4, pp. 374–379, May 1968.
Y. Kamiya, “Construction of a low parameter and disturbance sensitivity system by a model-following method,” IJC, vol. 23, no. 4, pp. 515–524, 1976.
I.H. Khalifa and A.A.R. Hanafy, “A note on trajectory sensitivity reduction using a three-term controller,” IEEE-TAC, vol. AC-29, no. 8, pp. 739–740, Aug. 1984. Errata, ibid., vol. AC-31, no. 1, pp. 93–94, Jan. 1986.
D.L. Kleinman and P. Krishna Rao, “An information matrix approach for aircraft parameter-insensitive control,” in Proc. IEEE Conf. on Decision and Contr., 1977.
E. Kreindler, “On minimization of trajectory sensitivity,” IJC, vol. 8, no. 1, pp. 89–96, 1968.
E. Kreindler, “Formulation of the minimum trajectory sensitivity problem,” IEEE-TAC, vol. AC-14, pp. 206–207, April 1969.
C.T. Leondes and P. Pezet, “Sensitivity requirements for suboptimal controllers,” IEEE-TAC, vol. AC-20, no. 3, pp. 426–428, June 1975.
C.T. Leondes and T.K. Sui, “Payoff sensitivity of linear quadratic differential games to parameter change,” ASME-JDSMC, vol. 103, pp. 36–38, March 1981.
J.F. Lowinger and J.A. Gibson, “Desensitizing algorithms for state-restrained optimal control assessments,” IJC, vol. 21, no. 3, pp. 353–373, 1975.
J.Y.S. Luh and E.R. Cross, “Optimal controller design for minimum trajectory sensitivity,” IJC, vol. 7, no. 6, pp. 557–568, 1968.
M.M. Missaghie and F.W. Fairman, “Sensitivity reducing observers for optimal feedback control,” IEEE-TAC, vol. AC-22, no. 6, pp. 952–957, Dec. 1977.
M.M. Missaghie and F.W. Fairman, “Desensitizing observers for LQG feedback control,” IJSS, vol. 12, no. 2, pp. 161–175, 1979.
R.B. Newell and D.B. Fisher, “Experimental evaluation of optimal, multivariable regulatory controllers with model-following capabilities,” Automatica, vol. 8, pp. 247–262, 1972.
M.M. Newmann, “On attempts to reduce the sensitivity of the optimal linear regulator to a parameter change,” ITC, vol. 11, no. 6, pp. 1079–1084, 1970.
K. Okada and R.E. Skelton, “Sensitivity controller for uncertain systems,” JGCD, vol. 13, no. 2, pp. 321–329, 1990.
J. O’Reilly, “Low-sensitivity feedback controllers for linear systems with incomplete state information,” IJC, vol. 29, no. 6, pp. 1047–1058, 1979.
A.I. Petrov, A.G. Zubov, and V.V. Minin, “Analysis of trajectory sensitivity of adaptive stochastic control systems,” SJAIS, vol. 18, no. 2, pp. 50–59, 1985.
S.G. Rao and A.C. Soudack, “Synthesis of optimal control systems with near sensitivity feedback,” IEEE-TAC, vol. AC-16, pp. 194–196, April 1971.
J.H. Rillings and R.J. Roy, “Analog sensitivity design of Saturn V launch vehicle,” IEEE-TAC, vol. AC-15, no. 4, pp. 437–442, Aug. 1970.
M. Saif, “Stability constrained robust linear regulator,” CAC, vol. 16, no. 3, pp. 66–69, 1988.
M. Saif, “Design of a trajectory insensitive regulator with prescribed degree of stability,” ASME-JDSMC, vol. 112, pp. 513–516, Sept. 1990.
P. Sannuti and J.B. Cruz, Jr., “A note on trajectory sensitivity of optimal control systems,” (with reply by A.J. Bradt) IEEE-TAC, vol. AC-13, pp. 111–113, Feb. 1968.
V.V.S. Sarnia and B.L. Deekshatulu, “Sensitivity design of optimal linear systems,” IJC, vol. 8, no. 6, pp. 653–658, 1968.
M.E. Sezer and D.D. Siljak, “Sensitivity of large-scale control systems,” JFI, vol. 312, nos. 3 /4, pp. 179–197, Sept/Oct. 1981.
P. Stavmulakis and P.E. Sarachik, “Low sensitivity feedback gains deterministic and stochastic control systems,” IJC, vol. 19, no. 1, pp. 15–31, 1974.
R. Subbayyan, V.V.S. Sarma, and M.C. Vaithilingam, “Trajectory sensitivity modification in optimal linear systems,” IEEE-TAC, vol. AC-22, no. 4, pp. 657–659, Aug. 1977.
R. Subbayyan, V.V.S. Sarma, and M.C. Vaithilingam, “An approach for sensitivity-reduced design of linear regulators,” IJSS, vol. 9, no. 1, pp. 65–74, Jan. 1978.
R. Subbayyan and M.C. Vaithilingam, “Sensitivity-reduced design of linear regulators,” IJC, voL 29, no. 3, pp. 435–440, 1979.
S.D. Weinrich and L. Lapidus, “Optimally sensitive and adaptive control systems,” AIChe J., vol. 17, no. 6, pp. 1471–1480, Nov. 1971.
C.A. Winsor and R.J. Roy, “The application of specific optimal control to the design of desensitized model following control systems,” IEEE-TAC, vol. AC-15, no. 3, pp. 326–333, June 1970.
S.C. Yang and W.L. Garrard, “A low sensitivity, modern approach to the longitudinal control of automated transit vehicles,” ASME-JDSMC, vol. 96, pp. 218–228, June 1974.
[E] Sensitivity with Respect to System - Auxiliary Parameters
Also consult Section [C] of the references in this chapter.
Y. Bar-Ness, “Pole sensitivity of the quadratic optimal regulator,” Elect. Len., voL 12, no. 13, pp. 341–343, June 1976.
Y.V. Kosyuk, “Analysis of nonstationary control systems by the method of `frozen’ coefficients,” SAC, vol. 3, no. 6, pp. 19–27, 1970.
K. Sugimoto and Y. Yamamoto, “Generalized robustness of optimality of linear quadratic regulators,” IJC, vol. 51, no. 3, pp. 521–533, 1990. Corrections, ibid., vol. 52, no. 5, pp. 1277–1278, 1990.
D.F. Wilkie and H.M. Van Schieveen, “On the sensitivity of the linear state regulator,” IJC, vol. 12, no. 4, pp. 709–719, 1970.
[F] Sensitivity Reduction and/or Optimization: Other Methods and Applications
P.R. Belanger, “Some aspects of control tolerances and first-order sensitivity in optimal control systems,” IEEE-TAC, vol. AC-11, no. 1, p. 77–83, 1966.
P.R. Belanger, “A paper machine color control system design using modern techniques,” IEEE- TAC, vol. AC-14, no. 6, pp. 610–616, Dec. 1969.
C.S. Berger, “Robust controller design by minimisation of the variation of the coefficients of the closed-loop characteristic equation,” Proc. IEE, vol. 131, Pt. D, no. 3, pp. 103–107, May 1984.
C.S. Berger,,“Robust control of discrete systems,” Proc. IEE, vol. 136, Pt. D, pp. 165–170, July 1989.
S.P. Bingulac, “On the role of orthonormality of sensitivity functions in parameter optimization problems,” Automatica, vol. 5, pp. 513–517, 1969.
V.A. Bodner, V.I. Vasil’ev, and F.A. Shaimardanov, “An algorithmic method of synthesis of a low-sensitive automatic control system,” ARC, no. 4, pp. 529–533, April 1974.
A. Burzio and D.D. Siljak, “Minimization of sensitivity with stability constraints in linear control systems,” IEEE-TAC, vol. AC-11, no. 3, pp. 567–569, July 1967.
E.M. Butler and R.A. Rohrer, “On relative sensitivity for certain linear optimal control problems,” in Proc. Asilomar Conf., vol. 279–286, 1968.
G.W. Carlock and A.P. Sage, “Sensitivity and error analysis algorithms for combined estimation and control systems,” IJC, vol. 21, no. 3, pp. 417–441, 1975.
S.S.L. Chang and P.E. Barry, “Optimal control of systems with uncertain parameters,” in Proc. IFAC, vol. 3 (of the 5th Congress), pp. 31.6.1–31.6. 5, 1972.
D.J. Cloud and B. Kouvaritakis, “Weighting sequences, optimal truncation and optimal frequency-response uncertainty bounds,” Proc. IEE, vol. 134, Pt. D, no. 3, pp. 153–170, May 1987.
J.B. Cruz, Jr., “Probabilistic sensitivity properties of neighboring optimal feedback systems,” Iran. J. Sei amp Tech., vol. 3, no. 4, pp. 271–282, 1975.
A.R. Daniels, Y.B. Lee, and M.K. Pal, “Nonlinear power-system optimisation using dynamic sensitivity analysis,” Proc. IEE, vol. 123, no. 4, pp. 365–370, 1976.
A.R. Daniels, Y.B. Lee, and M.K. Pal, “Combined suboptimal excitation control and governing of a.c. turbogenerators using dynamic sensitivity analysis,” Proc. IEE, vol. 124, no. 5, pp. 473–478, May 1977.
M. Darwish, J.D. Delacour, and J. Fantin, “Sensitivity analysis of optimal regulators with application to large scale power systems,” JASE, vol. 2, no. 4, pp. 259–268, Dec. 1977.
R.M. DeSantis and J. Conan, “Practical sensitivity reduction tests with application to power systems,” IJSS, vol. 8, no. 9, pp. 1067–1080, 1977.
T.S. Dillon, K. Morsztyn, and T. Tun, “Sensitivity analysis of the problem of economic dispatch of thermal power systems,” IJC, vol. 22, no. 2, pp. 229–248, 1975.
T.S. Dillon and T. Tun, “Application of sensitivity methods to the problem of optimal control of hydro-thermal power systems,” JOCAM, vol. 2, pp. 117–143, 1981.
P. Dorato and A. Kestenbaum, “Application of game theory to the sensitivity design of systems with optimal controller structures,” in Proc. Allerton Conf., pp. 35–45, 1965.
], “Application of game theory to the sensitivity design of optimal systems,” IEEE- TAC, vol. AC-12, pp. 85–87, 1967.
M. El-Hodiri, “Sensitivity analysis for an optimal control problem,” IEEE-TAC, vol. AC-20, no. 2, pp. 251–252, April 1975.
M.M. Elmetwally and N.D. Rao, “Sensitivity analysis in the optimal design of sychronous machine regulators,” IEEE-PAS, vol-PAS 93, no. 5, pp. 1310–1317, Sept./Oct. 1974.
M.M. Elmetwally and N.D. Rao, “Low-sensitivity control of nuclear reactors,” Elect. Lett., vol. 11, no. 13, pp. 269–270, June 1975.
A.N. Ennachenko and R.M. Yusupov, The use of sensitivity functions in synthesizing linear multicoupled control systems,“ ECy, vol. 14, pp. 146–154, March/April 1976.
T. Fuji and N. Mizushima, “Robustness of the optimality property of an optimal regulator: Multi-input case,” IJC, vol. 39, no. 3, pp. 441–453, 1984.
A.T. Fuller and A.S.I. Zinober, “On the existence of constant-ratio trajectories in nominally time-optimal control systems subject to parameter variation,” JFI, voL 303, pp. 359–369, April 1977.
M. Gavrilovic, R. Petrovic, and D.D. Siljak, “Adjoint method in sensitivity analysis of optimal systems,” JFI, vol. 276, no. 1, pp. 26–38, July 1963.
V.I. Gorodetskiy, F.M. Zakharin, V.M. Ponomarev, and R.M. Yusupov, “Direct and inverse problems of sensitivity theory,” ECy, vol. 9, no. 5, pp. 935–942, Sept./Oct. 1971.
P.L. Graf and R. Shoureshi, “Gain-sensitivity augmentation for near-optimal control of linear parameter-dependent plants,” JGCD, vol. 13, no. 2, pp. 310–320, 1990.
A.W.J. Griffin, R.J. Paul, and C.G. Legge, “Direct-sensitivity method of solving boundary-value problems in optimal-control studies,” Proc. IEE, vol. 116, no. 9, pp. 1611–1612, Sept. 1969.
R.E. Griffin and A.P. Sage, “Sensitivity analysis of fixed point linear smoothing algorithms,” IJC, vol. 8, no. 4, pp. 321–337, 1968.
R.E. Griffin and A.P. Sage, “Sensitivity analysis of discrete filtering and smoothing algorithms,” AIAA J., voL 7, no. 10, pp. 1890–1897, 1969.
G. Guardabassi, A. Locatelli, C. Maffezzoni, and N. Schiavoni, “Computer-aided design of structurally constrained multivariable regulators Part 1: Problem statement, analysis and solution,” Proc. IEE, vol. 130, Pt. D, no. 4, pp. 155–164, July 1983.
G. Guardabassi, A. Locatelli, C. Maffezzoni, and N. Schiavoni, “Computer-aided design of structurally constrained multivariable regulators via parameter optimisation Part 2: Applications,” Proc. IEE, vol. 130, Pt. D, no. 4, pp. 165–172, July 1983.
N.J. Guinzy and A.P. Sage, “Identification and modelling of large-scale systems using sensitivity analysis,” IJC, vol. 17, no. 5, pp. 1073–1087, 1973.
A.H. Haddad, J.B. Cruz, Jr., and P.V. Kokotovic. Haddad, J.B. Cruz, Jr., and P.V. Kokotovic, “Design of control systems with random parameters,” IJC, vol. 13, no. 5, pp. 981–992, 1971.
M. Hassan and M.G. Singh, “A hierarchical model-following controller for certain non-linear systems,” IJSS, vol. 7, no. 7, p. 727–730, 1976.
M. Hassan and M.G. Singh, “Synchronous machine control using a two level model follower,” Automatica, vol. 13, pp. 173–176, March 1977.
D.R. Howard and Z.V. Rekasius, “Error analysis with the maximum principle,” IEEE-TAC, vol. Ac-9, pp. 223–229, July 1964.
C.L. Irwin and V. Komkov, “Sensitivity analysis and model optimization for reaction-diffusion systems,” JOTA, vol. 44, no. 4, pp. 569–584, 1984.
H. Ishitani and S. Yamamura, “Sensitivity analysis of optimal control systems,” EEJ, vol. 87, no. 12, pp. 63–74, 1967.
Y.B. Kadimov, E.Y. Kuliyev, and S.I. Myachin, “Some questions concerning the application of the sensitivity theory to an analysis of transient processes while simulating systems with distributed parameters on analog computers,” Proc. IFAC, vol. 3 (of the 5th Congress), pp. 31.4.1–31. 4. 9, 1972.
H.S. Kang, “Minimum sensitivity design of M.V. systems,” IJC, vol. 11, no. 5, pp. 791–801, 1970.
B.Y. Katkovnik, “Sensitivity of gradient networks,” ARC, no. 12, pp. 1983–1989, Dec. 1970.
J.M. Kelly, G. Leitmann, and A.G. Soldatos, “Robust control of base-isolated structures under earthquake excitation,” JOTA, vol. 53, no. 2, pp. 159–180, 1980.
D.L. Kleinman, “Solving the optimal attention allocation problem in manual control,” IEEE-TAC, vol. AC-21, no. 6, pp. 813–822, Dec. 1976.
P.V. Kokotovic, J.B. Cruz, Jr., J. E. Heller, and P. Sannuti, “Synthesis of optimally sensitive systems,” Proc. IEEE, vol. 56, pp. 1318–1324, 1968.
V. Komkov and N. Coleman, “Optimality of design and sensitivity analysis of beam theory,” IJC, vol. 18, no. 4, pp. 731–740, 1973.
D.V. Lebedev, “Sensitivity of parameters of plant motion to errors of inertial navigation and control system,” SAC, vol. 9, pp. 41–47, Nov./Dec. 1976.
C.-K. Lee and C.-T. Chen, “Sensitivity comparisons of various analogue computer simulations,” IJC, vol. 10, no. 2, pp. 227–233, 1969.
N.G. Malek, O.T. Tan, P.M. Julich, and E.C. Tacker, “Trajectory-sensitivity design of load-frequency control systems,” Proc. IEE, vol. 120, no. 10, pp. 1273–1277, 1973.
J.E. Marshall and S.V. Salehi, “Improvement of system performance by the use of time-delay elements,” Proc. IEE, vol. 129, Pt. D, no. 5, pp. 177–181, Sept. 1982. Comments, with reply, by P.H. Landers, ibid., vol. 130, Pt. D, no. 2, p. 92, March 1983.
K. Nordstrom, “Trade-off between noise sensitivity and robustness for LQG regulators,” IJC, vol. 46, no. 5, pp. 1689–1714, 1987.
D.E. Olson and I.M. Horowitz, “Design of dominant-type control systems with large parameter variations,” IJC, vol. 12, no. 4, pp. 545–554, 1970.
C.S. Padilla and J.B. Cruz, Jr., “A linear dynamic feedback controller for stochastic systems with unknown parameters,” IEEE-TAC, vol. AC-22, no. 1, pp. 50–55, 1977.
C.S. Padilla and J.B. Cruz, “Sensitivity adaptive feedback with estimation redistribution,” IEEE-TAC, vol. AC-23, no. 3, pp. 445–451, 1978.
C.S. Padilla, J.B. Cruz, Jr., and R.A. Padilla, “A simple algorithm for SAFER control,” IJC, vol. 32, no. 6, pp. 1111–1118, 1980.
P.N. Paraskevopoulos, “Sensitivity reduction in exact model–matching of linear multivariable systems,” JFI, vol. 305, no. 2, pp. 99–118, Feb. 1978.
P.N. Paraskevopoulos, “Decoupling controller design via exact model–matching techniques,” Proc. IEE, vol. 125, no. 11, pp. 1285–1289, Nov. 1978.
H.J. Payne, E. Polak, D.C. Collins, and W.S. Meisel, “An algorithm for bicriteria optimization based on the sensitivity function,” IEEE-TAC, vol. AC-20, no. 4, pp. 546–548, Aug. 1975.
D.C. Reddy, “General sensitivity-reduction criterion for single-input multiple-output systems,” Elect. Leu., vol. 6, pp. 86–87, Feb. 1970.
J. Rissanen, “Drift compensation of linear systems by parameter adjustments,” ASME-JBE, pp. 415–418, June 1966.
P. Ronge, “Performance index sensitivity of optimal control systems with uncertain parameters,” JOCAM, vol. 6, pp. 359–384, 1985.
J. Rootenberg, “The sensitivity of optimally designed control systems, with minimum fuel performance index,” IJC, vol. 20, no. 1, pp. 101–112, 1974.
J. Rootenberg and P. Courtin, “System sensitivity for optimal problems with singular control,” IJC, vol. 20, no. 5, pp. 787–800, 1974.
M.V. Rybashov, “Insensitivity of gradient systems in the solution of linear problems on analog computers,” ARC, no. 10, pp. 1679–1687, Oct. 1969.
M.P. Sakharov, “Simplification of sensitivity models in the design of self-adjusting and adaptive systems,” ARC, vol. 29, no. 5, pp. 743–747, May 1968.
M.P. Sakharov, “Application of simplification conditions of sensitivity models in the design of nonscanning adaptive systems,” ARC, vol. 32, pp. 1080–1086, July 1971.
M.P. Sakharov, “On parameter adaptation algorithms for simplified sensitivity models,” ARC, vol. 32, no. 10, pp. 1664, 1669, Oct. 1971.
A.A. Sbaiti and A.P. Sage, “System optimization using quasilinearization and sensitivity analysis,” IJC, vol. 16, no. 2, pp. 343–352, 1972.
[71] D.B. Schaechter, “Closed-loop control performance sensitivity to parameter variations,” JGCD,vol. 6, no. 5, pp. 399–402, 1983.
L.A. Shirokov, “Parametric optimization with an ideal reference model,” SAC, vol. 15, no. 5, pp. 26–30, 1970.
D.D. Siljak and R.C. Dorf, “On the minimization of sensitivity in optimal control systems,” in Proc. Allerton Conf., pp. 225–229, 1965.
C.S. Sims and J.L. Melsa, “Sensitivity reduction in specific optimal control by the use of a dynamical controller,” IJC, vol. 8, pp. 491–502, 1968.
R.T. Stefani, “Reducing the sensitivity to parameter variations of a minimum-order reduced-order observer,” IJC, vol. 35, no. 6, pp. 983–995, 1982.
M.G. Strintzis and B. Liu, “Sensitivity minimization in the design of linear multivariable feedback systems,” in Proc. Allerton Conf., pp. 163–172, 1970.
A. Swiemiak, “State-inequalities approach to control systems with uncertainty,” Proc. IEE, vol. 129, Pt. D, no. 6, pp. 271–275, Nov. 1982.
A. Swiemiak, “Control laws for systems with inequality models of uncertainty,” Proc. IEE, vol. 133, Pt. D, no. 4, pp. 153–158, July 1986.
D.R. Towill and Z. Mehdi, “A new approach to system transient response sensitivity,” IJC, vol. 15, no. 2, pp. 319–331, 1972.
T.-P. Tsai and T.-S. Wang, “Optimal design of non-minimum-phase control systems with large plant uncertainty,” IJC, vol. 45, no. 6, pp. 2147–2159, 1987.
A.K. Tugcu, O. Coskunoglu, and R.E. Reid, “Performance criterion sensitivity analysis of ship-steering models with respect to shaping filter design parameters,” JOCAM, vol. 6, pp. 77–90, 1985.
S.G. Tzafestas, “Model-matching multicontroller design of reduced sensitivity,” ACTA, vol. 3, no. 3, pp. 67–69, Sept. 1975.
S.G. Tzafestas and P.N. Paraskevopoulos, “A sensitivity approach to the decoupling of linear systems with parameter disturbances,” in Proc. Joint Auto. Contr., pp. 92–100, 1973.
S.S. Venkata, W.J. Eccles, and J.H. Noland, “Multi-parameter sensitivity analysis of power-system stability by Popov’s method,” IJC, vol. 17, no. 2, pp. 291–304, 1973.
M.J. Vilenius, “The application of sensitivity analysis to electrohydraulic position control servos,” ASME-JDSMC, vol. 105, pp. 77–82, Tune 1983.
J.C. Wauer, J.M.H. Bruckner, and C.H. Humphrey, “Airplane performance sensitivities to lateral and vertical profiles,” JGCD, vol. 4, no. 6, pp. 606–613, 1981. Errata, ibid., vol. 5, no. 2, p. 224, 1982.
A.I. Yermachenko, “Synthesis of linear control systems with limited sensitivity,” ECy, vol. 9, no. 5, pp. 943–948, Sept./Oct. 1971.
K.-K. D. Young, “Near insensitivity of linear feedback systems,” JFI, vol. 314, no. 2, pp. 129–142, 1982.
A.S.I. Zinober and A.T. Fuller, “The sensitivity of nominally time-optimal control systems to parameter variation,” IJC, vol. 17, no. 4, pp. 673–703, 1973.
[G] Optimal Inputs for System Identification! Auxiliary Inputs for System Control (The Effects of the Human Operator)
M. Aoki and R. Staley, “On input signal synthesis in parameter identification,” Automatica, vol. 6, pp. 431–440, 1970.
O. Berman, E. Modiano, and J.A. Schnabel, “Sensitivity analysis and robust regression in investment performance evaluation,” IJSS, vol. 15, no. 5, pp. 481–489, 1984.
C. Bonivento, “Structural insensitivity versus identifiability,” IEEE-TAC, vol. AC-18, no. 2, pp. 190–192, April 1973.
V.N. Bukov, “Optimal algorithms in problems with bounded controllable coordinates,” ECy, vol. 20, no. 2, pp. 133–140, 1982.
M. Eslami, “Optimal input (policy) for system identification versus system sensitivity reduction with plant-operator,” The Univ. of Wisconsin-Madison, Dept. of Elec. and Computer Eng’g, Tech. Report ECE-79–2, 27 pp., Jan. 1979.
M. Eslami, “Optimal input for identification versus sensitivity reduction of systems with large parameter variations,” JOTA, vol. 77, no. 3, pp. 591–612, June 1993.
R.M. Gagliardi, “Input selection for parameter identification in discrete systems,” IEEE-TAC, vol. AC-12, pp. 597–599, Oct. 1967.
N.D. Georganas, “Optimal inputs and sensitivities for nonlinear process parameter estimation using imbedding techniques,” IEEE-TAC, vol. AC-21, no. 3, pp. 415–417, June 1976.
J.C. Geromel and Ji. da Cruz, “On the robustness of optimal regulators for nonlinear discrete-time systems,” IEEE-TAC, vol. AC-32, no. 8, pp. 703–712, Aug. 1987.
R.E. Kalaba and K. Spingarn, “Optimal inputs and sensitivities for parameter estimation,” JOTA, vol. 11, no. 1, pp. 56–67, 1973.
R.E. Kalaba and K. Spingarn, “Optimal input system identification for nonlinear dynamic systems,” JOTA, vol. 21, no. 1, pp. 91–102, Jan. 1977.
V.S. Levadi, “Design of input signals for parameter estimation,” IEEE-TAC, vol. AC-11, pp. 205–211, April 1966.
K.Y. Lim and M. Eslami, “Adaptive controller designs for robot manipulator systems using Lyapunov direct method,” IEEE-TAC, vol. AC-30, pp. 1229–1233, Dec. 1985. Comments, with reply, by Y.H. Chen, ibid., vol. AC-32, no. 2, pp. 190–192, Feb. 1987, and, with reply, by R.H. Middelton, ibid., vol. AC-32, no. 8, p. 749, Aug. 1987.
K.Y. Lim and M. Eslami, “Adaptive controller design for robot manipulator systems yielding reduced Carte- sian error,” IEEE-TAC, vol. AC-32, no. 2, pp. 184–187, Feb. 1987. Correction, ibid., vol. AC-38, no. 2, p. 384, 1993.
K.Y. Lim and M. Eslami, “Robust adaptive controller designs for robot manipulator systems,” IEEE-JRA, vol. RA-3, no. 1, pp. 54–66, 1987. Correction, ibid., vol. RA-9, no. 1, p. 119, 1993.
A.A. Lopez-Toledo and M. Athans, “Optimal policies for identification of stochastic linear systems,” IEEE-TAC, vol. AC-20, pp. 754–765, Dec. 1975.
R.K. Mehra, “Synthesis of optimal inputs for multiinput/multioutput systems with process noise, Parts I and II,” Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, Tech. Rep. TR 649, Feb. 1974.
R.K. Mehra, “Optimal inputs for linear system identification,” IEEE-TAC, vol. AC-19, no. 3, pp. 192–200, June 1974. Comments, by M.B. Zarrop and G.C. Goodwin, ibid., vol. AC-20, no. 2, pp. 299–300, April 1975.
R.K. Mehra, “Optimal input signals for parameter estimation in dynamic systems-survey and new results,” IEEE-TAC, vol. AC-19, no. 6, pp. 753–768, Dec. 1974.
R.K. Mehra and D.G. Lainiotis, Eds., System Identification: Advances and Case Studies. New York: Academic Press, 1976. Reviewed by P. Eykhoff, IEEE-TAC, vol. AC-23, no. 4, p. 766, 1978.
N.E. Nahi and G. Napjus, “Design of optimal probing signals for vector parameter estimation,” in Proc. IEEE Conf. on Decision Contr., pp. 162–168, 1971.
N.E. Nahi and D.E. Wallis, Jr., “Optimal inputs for parameter estimation in dynamic systems with white observation noise,” in Proc. Joint Auto. Contr. Conf, pp. 506–512, 1969.
Y. Sawaragi and K. Ogino, “Sensitivity approach to optimal input synthesis for parameter identification of bilinear system,” in Proc. IFAC, vol. 3 (of the 5th Congress), pp. 31.2.131.2. 6, 1972.
F.C. Schweppe, “On the accuracy and resolution of radar signals,” IEEE-TAES, vol. AES-I, pp. 235–245, Dec. 1965.
Y. Stepanenko and J. Yuan, “Robust adaptive control of a class of nonlinear mechanical systems with unbounded and fast-varying uncertainties,” Automatica, vol. 28, no. 2, pp. 265–276, 1992.
K. Watanabe and D.M. Himmelblau, “Instrument fault detection in systems with uncertainties,” IJSS, vol. 13, no. 2, pp. 137–158, 1982.
C. Yaling, “Sensitivity operator and approximate algorithm for parameter estimation,” IJC, vol. 46, no. 2, pp. 537–546, 1987.
[H] Sensitivity Considerations in Hardy Spaces
Also consult references on disturbance rejection in § 6.12.K2; and on sensitivity issues in selected multidisciplinary optimization methods, and numerical methods in § 6.12.P; as well as entries on stability robustness analysis in § 5.12.E, and § 5.12.G.
[HI] Sensitivity Considerations in Hardy Spaces Pertinent References on Feedback System Design and Mathematics
Also consult references in § 6.12.A, § 2.9.A, and § 2.9.E.
V.M. Adamjan, D.Z. Arov, and M.G. Krein, “Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem,” Math. USSR Sbornik, vol. 15, pp. 31–73, 1971.
V.M. Adamjan, D.Z. Arov, and M.G. Krein, “Infinite Hankel block matrices and related extension problems,” Amer. Math. Soc. Translations, series 2, vol. 111, pp. 133–156, 1978.
J.A. Ball and J.W. Helton, “A Beurling-Lax theorem for the Lie group U(m, n) which contains most classical interpolation theory,” JOT, vol. 9, pp. 107–142, 1983.
J.J. Bongiorno, Jr., “Minimum sensitivity design of linear multivariable feedback control systems by matrix spectral factorization,” IEEE-TAC, vol. AC-14, pp. 665–573, 1969.
J.B. Conway, A Course in Functional Analysis. New York: Springer — Verlag, 1985.
P. Delsarte, Y. Genin, and Y. Kamp, “Schur parameterization of positive definite blockToeplitz systems,” SIAM-JAM, vol. 36, no. 1, pp. 34–46, 1979.
P. Delsarte, Y. Genin, and Y. Kamp, “The Nevanlinna-Pick problem for matrix-valued functions,” SIAM JAM, vol. 36, no. 1, pp. 47–61, 1979.
C.A. Desoer and W.S. Chan, “The feedback interconnection of lumped linear time-invariant systems,” JFI, vol. 300, nos. 5 amp 6, pp. 335–351, 1975.
C.A. Desoer, R.-W. Liu, J. Murray, and R. Saeks, “Feedback system design: The fractional representation approach to analysis and synthesis,” IEEE-TAC, vol. AC-25, no. 3, pp. 399412, 1980.
P.L. Duren, Theory of H“ Spaces. New York: Academic Press, 1970.
P. Koosis, Introduction to H p Spaces. Cambridge, England: Cambridge Univ. Press, 1980.
S.-Y. Kung and D.W. Lin, “Optimal Hankel-norm model reductions: Multivariable systems,” IEEE-TAC, vol. AC-26, no. 4, pp. 832–852, 1981.
Z. Nehari, “On bounded bilinear forms,” Annals of Mathematics, vol. 65, pp. 153–162, 1957.
R. Nevanlinna, Analytic Funstions. [Translated from German by P. Emig.] New York: Springer - Verlag, 1970.
R. Redheffer, “Inequalities for a matrix Riccati equation,” JMM, vol. 8, pp. 349–367, 1959.
R. Redheffer, “Supplementary notes on matrix Riccati equations,” JMM, vol. 9, pp. 745–748, 1960.
R.M. Redheffer, “On a certain linear fractional transformation,” JMP,vol. 39, pp. 269–286, 1960. [This is the same author as the preceding one.]
W.T. Reid, “Solutions of a Riccati matrix differential equation as functions of initial values,” JMM, vol. 8, pp. 221–230, 1959.
W.T. Reid, ‘Properties of solutions of a Riccati matrix differential equation,“ JMM, vol. 9, pp. 749–769, 1960.
D. Sarason, “Generalized interpolation in Hm, Trans. of American Mathematical Society, vol. 127, no. 2, pp. 179–203, 1967.
G. Stein and M. Athans, “The LQG/LTR procedure for multivariable feedback control design,” IEEE-TAC, vol. AC-32, no. 2, pp. 105–114, 1987.
B. Sz: Nagy and C. Foins, Harmonic Analysis of Operators on Hilbert Space. Amsterdam: North-Holland Publ., 1970.
M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985. Reviewed by B.F. Wyman, IEEE-TAC, vol. AC-31, no. 11, p. 1085, 1986, and by F.M. Callier, Automatica, vol. 22, no. 4, pp. 500–501, 1986.
J.C. Willems, “Least squares stationary optimal control and the algebraic Riccati equation,” IEEE-TAC, vol. AC-16, no. 6, pp. 621–634, 1971.
D.C. Youla, JJ. Bongiorno, Jr., and H.A. Jabr, “Modern Wiener-Hopf design of optimal controllers Part I: The single-input-output case,” IEEE-TAC, vol. AC-21, pp. 3–13, 1976.
D.C. Youla, H.A. Jabr, and J.J. Bongiorno, Jr., “Modern Wiener-Hopf design of optimal controllers-Part II: The multivariable case,” IEEE-TAC, vol. AC-21, pp. 319–338, 1976.
[H2] Sensitivity Considerations in Hardy Spaces Complex - Domain Approach
B. Bamieh, J.B. Pearson, B.A. Francis, and A. Tannenbaum, “A lifting technique for linear periodic systems with applications to sampled-data control,” SCL, vol. 17, pp. 79–88, 1991.
P. Boekhoudt, “Solution of polynomial equations in H„ optimal control,” CTAT, vol. 6, no. 3, pp. 321–337, 1990.
M.J. Englehart and M.C. Smith, “A four-block problem for H. design Properties and applications,” Automatica, vol. 27, no. 5, pp. 811–818, 1991.
N.A. Fairbaim and Mi. Grimble, H„ robust controller for self-tuning applications Part 3. Self-tuning controller implementation,“ IJC, vol. 52, no. 1, pp. 15–36, 1990.
D.S. Flamm and S.K. Mitter, H°° sensitivity minimization for delay systems,“ SCL, vol. 9, pp. 17–24, 1987.
C. Foias and A. Tannenbaum, “Weighted optimization theory for nonlinear systems,” SIAMJCO, vol. 27, no. 4, pp. 842–860, July 1989.
C. Foins, A. Tannenbaum, and G. Zames, “On decoupling the H°°-optimal sensitivity problem for products of plants,” SCL, vol. 7, pp. 239–245, 1986.
C. Foins, A. Tannenbaum, and G. Zames, “Weighted sensitivity minimization for delay systems,” IEEE-TAC, vol. AC-31, no. 8, pp. 763–766, Aug. 1986.
C. Foins, A. Tannenbaum, and G. Zames, “On the H°°-optimal sensitivity problem for systems with delays,” SIAM-JCO, vol. 25, no. 3, pp. 686–705, May 1987.
Y.K. Foo and L Postlethwaite, “An H”-minimax approach to the design of robust control systems,“ SCL, vol. 5, pp. 81–88, 1984.
Y.K. Foo and L Postlethwaite, “An H”-minimax approach to the design of robust control systems, Part II: All solutions, all-pass form solutions and the `best’ solution,“ SCL, vol. 7, pp. 261–268, 1986.
B.A. Francis, A Course in H„ Control Theory. New York: Springer - Verlag, 1987. Reviewed by G. Conte, IEEE-TAC,vol. AC-32, no. 12, pp. 1144–1145, 1987, and by P.P. Khargonekar, SIAM R.,voL 30, no. 2, pp. 335–336, 1988.
B.A. Francis and J.C. Doyle, “Linear control theory with an H„ optimality criterion,” SIAMJCO, vol. 25, no. 4, pp. 815–844, July 1987.
B.A. Francis, J.W. Helton, and G. Zames, H“-optimal feedback controllers for linear multivariable systems,” IEEE-TAC, vol. AC-29, no. 10, pp. 888–900, Oct. 1984.
B.A. Francis and G. Zames, “On H°°-optimal sensitivity theory for SISO feedback systems,” IEEE-TAG, vol. AC-29, no. 1, pp. 9–16, Jan. 1984.
D. Fragopoulos, M.J. Grimble, and U. Shaked, H„ controller design for the SISO case using a Wiener approach,“ IEEE-TAC, voL AC-36, no. 10, pp. 1204–1208, 1991.
K. Glover, D.J.N. Limbeer, J.C. Doyle, E.M. Kasenally, and M.G. Safonov, “A characterization of all solutions to the four block general distance problem,” SIAM-KO, vol. 29, no. 2, pp. 283–324, 1991.
M. Green, H„ controller synthesis by J-lossless coprime factorization,“ SIAM-KO, vol. 30, no. 3, pp. 522–547, 1992.
M.J. Grimble, H„ robust controller for self-tuning control applications Part 1. Controller design,“ IJC, vol. 46, no. 4, pp. 1429–1444, 1987.
M.J. Grimble, H robust controller for self-tuning control applications Part 2. Self-tuning and robustness,“ IJC, vol. 46, no. 5, pp. 1819–1840, 1987.
M.J. Grimble, “Optimal H„ multivariable robust controllers and the relationship to LQG design problems,” IJC, vol. 48, no. 1, pp. 33–58, 1988.
M.J. Grimble, “Extensions to H„ multivariable robust controllers and the relationship to LQG design problems,” IJC, vol. 50, no. 1, pp. 309–338, 1989.
M.J. Grimble,, “Predictive H„ model reference optimal control law for SISO systems,” Proc. IEE, vol. 136, Pt. D, no. 6, pp. 273–284, Nov. 1989.
], M.J. Grimble, “Generalised H„ multivariable controllers,” Proc. IEE, vol. 136, Pt. D, no. 6, pp. 285–297, Nov. 1989.
M.J. Grimble, “Comments on Stem’s postulated high-frequency behavior of H°° optimal controll- ers,” IEEE-TAC, vol. AC-35, no. 6, pp. 762–765, June 1990. Comments by J.M. Krause, ibid., vol. AC-37, no. 5, p. 702, 1992.
M.J. Grimble, “Hm controllers with a PID structure,” ASME-JDSMC, vol. 112, pp. 325–336, Sept. 1990.
M.J. Grimble, “H„ observations weighted control law, ASME-JDSMC, vol. 112, pp. 337–348, Sept. 1990.
S. Hara and T. Sugie, “Inner-outer factorization for strictly proper functions with jco-axis zeros,” SCL, vol. 16, pp. 179–185, 1991.
S. Hara, T. Sugie, and R. Kondo, H„ control problem with jtw-axis zeros,“ Automatica, vol. 28, no. 1, pp. 55–70, 1992.
J.W. Helton, “Worst case analysis in the frequency domain: The H°° approach to control,” IEEE-TAC, vol. AC-30, no. 12, pp. 1154–1170, Dec. 1985.
H. Ito, H. Ohmori, and A. Sono, “Design of stable controllers attaining low H°° weighted sensitivity,” IEEE-TAC, vol. AC-38, no. 3, pp. 485–488, 1993.
P.P. Khargonekar and A. Tannenbaum, “Non-Euclidian matrices and robust stabilization of systems with parameter uncertainty,” IEEE-TAC, vol. AC-30, pp. 1005–1013, Oct. 1985.
R. Kondo and S. Hara, “On cancellation in H„ optimal controllers,” SCL, vol. 13, pp. 205210, 1989.
H. Kwakernaak, “A polynomial approach to minimax frequency domain optimization of multivariable feedback systems,” IJC, vol. 44, no. 1, pp. 117–156, 1986.
D.K. Le and A.E. Frazho, “A numerical procedure for a non-rational H°°-optimization problem in control design,” SCL, vol. 16, pp. 9–15, 1991.
K.E. Lenz, “Simple mixed sensitivity optimal controllers,” SCL, vol. 17, pp. 363–373, 1991.
K.E. Lenz, P.P. Khargonekar, and J.C. Doyle, “When is a controller H”-optimal?“ MCSS, vol. 1, pp. 107–122, 1988.
G.M.H. Leung, T.P. Perry, and B.A. Francis, “Performance analysis of sampled-data control systems,” Automatica, vol. 27, no. 4, pp. 699–704, 1991.
D.W. Luse and J.A. Ball, “Frequency-scale decomposition of H°°-disk problems,” SIAMJCO, vol. 27, no. 4, pp. 814–835, July 1989.
R.I. Ober and J.A. Sefton, “Stability of control systems and graphs of linear systems,” SCL, vol. 17, pp. 265–280, 1991.
Y. Ohta, H. Maeda, and S. Kodama, “Unit interpolation in H,,: Bounds of norm and degree of interpolants,” SCL, vol. 17, pp. 251–256, 1991.
Y. Ohta, G. Tadmor, and S.K. Mister, “Sensitivity reduction over a frequency band,” IJC, vol. 48, no. 5, pp. 2129–2138, 1988.
S.D. O’Young and B.A. Francis, “Sensitivity tradeoffs for multivariable plants,” IEEE-TAC, vol. AC-30, no. 7, pp. 625–632, July 1985.
S.D. O’Young, I. Postlethwaite, and D.-W. Gu, “A treatment of jte-axis model-matching transformation zeros in the optimal H2 and H°° control designs,” IEEE-TAC, vol. AC-34, no. 5, pp. 551–553, May 1989.
H. Ozbay and A. Tannenbaum, “On the structure of suboptimal H°° controllers in the sensitivity minimization problem for distributed stable plants,” Automatica, vol. 27, no. 2, pp. 293–305, 1991.
J.R. Partington and K. Glover, “Robust stabilization of delay systems by approximation of coprime factors,” SCL, vol. 14, pp. 325–331, 1990.
L. Qiu and Ei. Davison, “Feedback stability under simultaneous gap metric uncertainties in plant and controller,” SCL, vol. 18, pp. 9–22, 1992.
S. Raman and E.-W. Bai, “A linear, robust and convergent interpolatory algorithm for quantifying model uncertainties,” SCL, vol. 18, pp. 173–177, 1992.
R. Ravi, A.M. Pascoal, and P.P. Khargonekar, “Normalized coprime factorizations for linear time-varying systems,” SCL, vol. 18, pp. 455–465, 1992.
M. Saeki, “Methods of solving a polynomial equation for an H°° optimal control problem for a single-input single-output discrete-time system,” IEEE-TAC, vol. AC-34, no. 2, pp. 166–168, Feb. 1989.
M. Saeki, H“/LTR procedure with specified degree of recovery,” Automatisa, vol. 28, no. 3, pp. 509–517, 1992.
M.G. Safonov and V.X. Le, “An alternative solution to the H„-optimal control problem,” SCL, vol. 10, pp. 155–158, 1988.
J. Sefton and K. Glover, “Pole/zero cancellations in the general H„ problem with reference to a two block design,” SCL, vol. 14, pp. 295–306, 1990.
U. Shaked, “The explicit structure of inner matrices and its applications in H°°-optimization,” IEEE-TAC, vol. AC-34, no. 7, pp. 734–738, July 1989.
M.C. Smith, “Well-posedness of H°° optimal control problems,” SIAM-JCO, vol. 28, no. 2, pp. 342–358, March 1990.
T. Sugie and S. Hara, H„-suboptimal control problem with boundary constraints,“ SCL, vol. 13, pp. 93–99, 1989.
G. Tadmor, “An interpolation problem associated with H°°-optimal design in systems with distributed input lags,” SCL, vol. 8, pp. 313–319, 1987.
M.C. Tsai, E.J.M. Geddes, and I. Postlethwaite, “Pole-zero cancellations and closed-loop properties of an H°° mixed sensitivity design problem,” Automatica, vol. 28, no. 3, pp. 519–530, 1992.
L.Y. Wang and G. Zames, “Lipschitz continuity of H°° interpolation,” SCL, vol. 14, pp. 381387, 1990.
N.E. Wu and G. Gu, “Discrete Fourier transform and H°°-approximation,” IEEE-TAC, vol. AC-35, no. 9, pp. 1044–1046, Sept. 1990.
Q.-H. Wu and M. Mansour, “Robust output regulation for a class of linear multivariable systems,” SCL, vol. 13, pp. 227–232, 1989.
Q.-H. Wu and M. Mansour, “Decentralized robust output regulation using H”-optimization techniques,“ CTAT, vol. 6, no. 2, pp. 187–214, 1990.
Q.-H. Wu and M. Mansour, H°°-optimal solutions of robust regulator problem for linear MIMO systems,“ IJC, vol. 52, no. 5, pp. 1241–1262, 1990.
I. Yaesh and U. Shaked, “Nondefinite least squares and its relation to H„-minimum error state estimation,” IEEE-TAC, vol. AC-36, no. 12, pp. 1469–1472, 1991.
J.-S. Young, C.E. Lin, and F.-B. Yeh, “Characterization of the sub-layers for 2-block H”-optimal control problem,“ SCL, vol. 15, pp. 193–198, 1990.
G. Zanies, “Feedback and optimal sensitivity: Model reference transformation, multiplicative seminorms, and approximate inverses,” IEEE-TAC, vol. AC-26, no. 2, pp. 301–320, April 1981.
G. Zames and D. Bensoussan, “Multivariable feedback, sensitivity, and decentralized control,” IEEE-TAC, vol. AC-28, no. 11, pp. 1030–1035, Nov. 1983.
G. Zames and B.A. Francis, “Feedback, minimax sensitivity, and optimal robustness,” IEEE-TAC, vol. AC-28, no. 5, pp. 585–601, May 1983.
[H3] Sensitivity Considerations in Hardy Spaces State - Space Approach
D.S. Bernstein and W.M. Haddad, “LQG control with an H°° performance bound: A Riccati approach,” IEEE-TAC, vol. AC-34, no. 3, pp. 293–305, March 1989.
P.M.M. Bongers and O.H. Bosgra, “Normalized coprime factorizations for systems in generalized state-space form,” IEEE-TAC, vol. AC-38, no. 2, pp. 348–350, 1993.
B.-C. Chang, “A stable state-space realization in formulation of H°° norm computation,” IEEE-TAC, vol. AC-32, no. 9, pg. 811–815, Sept. 1987.
C.E. de Souza, M. Fu, and L. Xie, H m analysis and synthesis of discrete-time systems with time-varying uncertainty,“ IEEE-TAC, vol. AC-38, no. 3, pp. 459–462, 1993.
C.E. de Souza and L. Xie, “On the discrete-time bounded real lemma with application in the characterization of static state feedback H„ controllers,” SCL, vol. 18, pp. 61–71, 1992.
J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis, “State-space solutions to standard H2 and H°° control problems,” IEEE-TAC vol. AC-34, pp. 831–847, Aug. 1989. [cf., [27 and 56].]
M.K.H. Fan and A.L. Tits, “A measure of worst-case H„ performance and of largest acceptable uncertainty,” SCL, vol. 18, pp. 409–421, 1992.
M.K.H. Fan, AL. Tits, and J.C. Doyle, “Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics,” IEEE-TAC, vol. AC-36, no. 1, pp. 25–38, 1991.
B.A. Francis and J.C. Doyle, “Linear control theory with an H., optimality criterion,” SIAMJCO, voL 25, no. 4, pp. 815–844, July 1987.
K. Glover and J.C. Doyle, “State-space formulae for all stabilizing controllers that satisfy an H„-norm bound and relations to risk sensitivity,” SCL, vol. 11, pp. 167–172, 1988.
M. Green, K. Glover, D.J.N. Limebeer, and J.C. Doyle, “A J-spectral factorization approach to H”“ control,” SIAM-JCO, vol. 28, pp. 1350–1371, 1990.
W.M. Haddad and D.S. Bernstein, “Generalized Riccati equations for the full-and reduced-order mixed-norm H2/H„ standard problem,” SCL, vol. 14, pp. 185–197, 1990.
W.M. Haddad and D.S. Bernstein, “Robust stabilization with positive real uncertainty: Beyond the small gain theorem,” SCL, vol. 17, pp. 191–208, 1991.
H.S. Hvostov, “Simplifying H”“ controller synthesis via classical feedback system structure,” IEEE-TAC, vol. AC-35, no. 4, pp. 485–488, April 1990.
Y.S. Hung and B. Pokrud, “An H” approach to feedback design with two objective functions,“ IEEE-TAC, vol. AC-37, no. 6, pp. 820–824, 1992.
P.A. Iglesias, D. Mustafa, and K. Glover, “Discrete time H„ controllers satisfying a minimum entropy criterion,” SCL, vol. 14, pp. 275–286, 1990.
P.P. Khargonekar, K.M. Nagpal, and K.R. Poona, H„ control with transients,“ SIAM-KO, vol. 29, no. 6, pp. 1373–1393, 1991.
P.P. Khargonekar, I.R. Petersen, and M.A. Rotes, H„-optimal control with state-feedback,“ IEEE-TAC, vol. AC-33, no. 8, pp. 786–788, 1988.
P.P. Khargonekar, I.R. Petersen, and K. Zhou, “Robust stabilization of uncertain linear systems: Quadratic stabilizability and H” control theory,“ IEEE-TAC, vol. AC-35, no. 3, pp. 356–361, 1990.
P.P. Khargonekar and M.A. Rotea, “Multiple objective optimal control of linear systems: The quadratic norm case,” IEEE-TAC, vol. AC-36, no. 1, pp. 14–24, 1991.
P.P. Khargonekar and M.A. Rotea, “Mixed H2/ H., control: A convex optimization approach,” IEEE-TAC, vol. AC- 36, no. 7, pp. 824–837, 1991.
H. Kimura, Y. Lu, and R. Kawatani, “On the structure of H°° control systems and related extensions,” IEEE-TAC, vol. AC-36, no. 6, pp. 653–667, 1991.
V.X. Le and M.G. Safonov, “Rational matrix GCD’s and the design of squaring-down compensators–A state-space theory,” IEEE-TAC, vol. AC-37, no. 3, pp. 384–392, 1992.
D.J.N. Limebeer and G.D. Halikias, “A controller degree bound for H°°-optimal control problems of the second kind,” SIAM-JCO, vol. 26, no. 3, pp. 646–677, 1988.
D.J.N. Limebeer and Y.S. Hung, “An analysis of the pole-zero cancellations in H°°-optimal problems of the first kind,” SIAM-JCO, vol. 25, no. 6, pp. 1457–1493, 1987.
A.N. Madiwale, W.M. Haddad, and D.S. Bernstein, “Robust H” control design for systems with structured parameter uncertainty,“ SCL, vol. 12, pp. 393–407, 1989.
T. Mita, K.Z. Liu, and S. Ohuchi, “Correction of the FI results in H., control and parameterization of H„ state feedback controllers,” IEEE-TAC, vol. AC-38, no. 2, pp. 343–347, 1993.
J.B. Moore and T.T. Tay, “Loop recovery via H`°IH 2 sensitivity recovery,” IJC, vol. 49, no. 4, pp. 1249–1271, 1989.
D. Mustafa, “Relations between maximum-entropy /H.. control and combined H.,/LQG control,” SCL, vol. 12, pp. 193–203, 1989.
D. Mustafa and K. Glover, “Controller reduction by H„-balanced truncation,” IEEE-TAC, vol. AC-36, no. 6, pp. 668–682, 1991.
D. Mustafa and K. Glover, Minimum Entropy H„ Control. Berlin: Springer–Verlag, 1990. Reviewed by D.S. Bernstein, IEEE-TAC, vol. AC-37, no. 8, pp. 1276–1277, 1992, and by J.A. Ball, SIAM R., vol. 35, no. 4, pp. 652–655, Dec. 1993.
D. Mustafa, K. Glover, and D.J.N. Limebeer, “Solutions to the H. general distance problem which minimize an entropy integral,” Automatica, vol. 27, no. 1, pp. 193–199, 1991.
I.R. Petersen, “Disturbance attenuation and H°° optimization: A design method based on the algebraic Riccati equation,” IEEE-TAC, vol. AC-32, no. 5, pp. 427–429, May 1987.
I.R. Petersen and C. Hollot, “High gain observers applied to problems in the stabilization of uncertain linear systems, disturbance attenuation and H°° optimization,” IJACSP, vol. 2, pp. 347–369, 1988.
R. Ravi, K.M. Nagpal, and P.P. Khargonekar, H°° control of linear time-varying systems: A state-space approach,“ SIAM-JCO, vol. 29, no. 6, pp. 1394–1413, 1991.
M.A. Rotea and P.P. Khargonekar, “H2-optimal control with an H’”-constraint: The state feedback case,“ Automatica, vol. 27, no. 2, pp. 307–316, 1991.
M.G. Safonov, D.J.N. Limebeer, and R.Y. Chiang, “Simplifying the H°° theory via loop-shifting, matrix-pencil and descriptor concepts,” IJC, vol. 50, no. 6, pp. 2467–2488, 1989.
C. Scherer, H°°-control by state-feedback and fast algorithms for the computation of optimal H`“-norms,” IEEE-TAC, vol. AC-35, no. 10, pp. 1090–1099, Oct. 1990.
G. Shi, Y. Zou, and C. Yang, “An algebraic approach to robust H°° control via state feedback,” SCL, vol. 18, pp. 365–370, 1992.
A.A. Stoorvogel, “The singular H2 control problem,” Automatica voL 28, no. 3, pp. 627–631, 1992.
G. Tadmor, “Uncertain feedback loops and robustness in general linear systems,” Automatica, vol. 27, no. 6, pp. 1039–1042, 1991.
H.T. Toivonen, “Sampled-data control of continuous-time systems with an H. optimality criterion,” Automatica, vol. 28, no. 1, pp. 45–54, 1992.
M.-C. Tsai, D.-W. Gu, and I. Postlethwaite, “A state-space approach to super-optimal H°° control problems,” IEEE-TAC, vol. AC-33, no. 9, pp. 833–843, Sept. 1988.
K. Uchida and M. Fujita, “Finite horizon H°° control problems with terminal penalties,” IEEE-TAC, vol. AC-37, no. 11, pp. 1762–1767, 1992.
A.J. van der Schaft, “On a state space approach to nonlinear H. control,” SCL, vol. 16, pp. 1–8, 1991.
A.J. van der Schaft, “L2-gain analysis of nonlinear systems and nonlinear state feedback H. control,” IEEE-TAC, vol. AC-37, no. 6, pp. 770–784, 1992.
D.J. Walker, “Relationship between three discrete-time H°° algebraic Riccati equation solutions,” IJC, vol. 52, no. 4, pp. 801–809, 1990.
L. Xie and C.E. de Souza, “State feedback H. optimal control problems for non-detectable systems,” SCL, vol. 13, pp. 315–319, 1989.
L. Xie and C.E. de Souza, “Robust H. control for linear time-invariant systems with norm-bounded uncer- tainty in the input matrix,” SCL, vol. 14, pp. 389–396, 1990.
L. Xie and C.E. de Souza, “Robust H. control for linear systems with norm-bounded time-varying uncer- tainty,” IEEE-TAC, vol. AC-37, no. 8, pp. 1188–1191, 1992.
I. Yaesh and U. Shaked, “Minimum H°°-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games,” IEEE-TAC, vol. AC-35, no. 9, pp. 1061–1064, Sept. 1990.
I. Yaesh and U. Shaked, H„-optimal one-step-ahead output feedback control of discrete-time systems,“ IEEE-TAC, vol. AC-37, no. 8, pp. 1245–1250, 1992.
H.-H. Yeh, S.S. Banda, and B.-C. Chang, “Necessary and sufficient conditions for mixed H2 and H. optimal control,” IEEE-TAC, vol. AC-37, no. 3, pp. 355–358, 1992.
H.-H. Yeh, S.S. Banda, S.A. Heise, and A.C. Bartlett, “Robust control design with real-parameter uncertainty and unmodeled dynamics,” JGCD, vol. 13, no. 6, pp. 1117–1125, 1990.
K. Zhou, “Comparison between H2 and H. controIlers,” IEEE-TAC, vol. AC-37, no. 8, pp. 1261–1265, 1992.
K. Zhou, “On the parameterization of H. controllers,” IEEE-TAC, vol. AC-37, no. 9, pp. 1442–1446, 1992.
K. Zhou and P.P. Khargonekar, “On the weighted sensitivity minimization problem for delay systems,” SCL, vol. 8, pp. 307–312, 1987.
K. Zhou and P.P. Khargonekar, “An algebraic Riccati equation approach to H°° optimization,” SCL, vol. 11, pp. 85–91, 1988.
[H4] Sensitivity Considerations in Hardy Spaces Operator Approach
J.A. Ball and N. Cohen, “Sensitivity minimization in an H°° norm: Parametrization of all suboptimal solutions,” IJC, vol. 45, no. 3, pp. 785–816, 1987.
J.A. Ball and A.C.M. Ran, “Optimal Hankel norm model reductions and Wiener-Hopf factorization I: The canonical case,” SIAM-KO, vol. 25, no. 2, pp. 362–382, 1987.
], “Optimal Hankel norm model reductions and Wiener-Hopf factorization II: The noncanonical case,” lEOT, vol. 10, pp. 416–436, 1987.
F. Fagnani, “An operator-theoretic approach to the mixed-sensitivity minimization problem,” SCL, vol. 17, pp. 227–235, 1991.
K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems and their L°°-error bounds,” IJC, vol. 39, no. 6, pp. 1115–1193, 1984.
K. Glover and D. McFarlane, “Robust stabilization of normalized coprime factor plant descriptions with H’”-bounded uncertainty,“ IEEE-TAC, vol. AC-34, pp. 821–830, 1989.
B. Hanzon, “The area enclosed by the (oriented) Nyquist diagram and the Hilbert-SchmidtHankel norm of a linear system,” IEEE-TAC, vol. AC-37, no. 6, pp. 835–839, 1992.
E.A. Jonckheere and J.-C. Juang, “Fast computation of achievable feedback performance in mixed sensitivity H`° design,” IEEE-TAC, vol. AC-32, no. 10, pp. 896–906, 1987.
D. McFarlane and K. Glover, “A loop shaping design procedure using H„ synthesis,” IEEE-TAC, vol. AC-37, no. 6, pp. 759–769, 1992.
G. Michaletzky, “Hankel-norm approximation of a rational function using stochastic realizations,” SCL, vol. 13, pp. 211–216, 1989.
H. Ozbay and A. Tannenbaum, “A skew Toeplitz approach to the N’” optimal control of multivariable distributed systems,“ SIAM-JCO, vol. 28, no. 3, pp. 653–670, May 1990.
M.G. Safonov and M.S. Verma, ’Z„ optimization and Hankel approximation,“ IEEE-TAC, vol. AC-30, no. 3, pp. 279–280, 1985.
C.-D. Yang and F.-B. Yeh, “An efficient algorithm on optimal Hankel-norm approximation for multivariable systems,” IEEE-TAC, vol. AC-37, no. 6, pp. 815–820, 1992.
J.-S. Young and C.E. Lin, “Construction of the maximal Schmidt pair for the 4-block H°°-optimal control problem,” IEEE-TAC, vol. AC-37, no. 8, pp. 1250–1252, 1992.
[H5] Sensitivity Considerations in Hardy Spaces Computational Issues and Optimization Approaches
T. Auba and Y. Funahashi, “Upper and lower bounds of Gramian for a class of perturbed linear systems,” IEEE-TAC, vol. AC-37, no. 10, pp. 1659–1661, 1992.
A.C. Antoulas, “On minimal realization: A polynomial approach,” SCL, vol. 14, pp. 319–324, 1990.
S. Boyd and V. Balakrishnan, “A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its Lm norm,” SCL, vol. 15, pp. 1–7, 1990.
S. Boyd, V. Balakrishnan, and P. Kabamba, “On computing the H„ norm of a transfer matrix,” in Proc. Amer. Contr. Conf., pp. 396–397, 1988.
S. Boyd, V. Balakrishnan, and P. Kabamba, “A bisection method for computing the If norm of a transfer matrix and related problems,” MCSS vol. 2, pp. 207–219, 1989. [cf., [P. 11 amp 12].]
N.A. Bruinsma and M. Steinbuch, “A fast algorithm to compute the H„-norm of a transfer function matrix,” SCL, vol. 14, pp. 287–293, 1990.
B.-C. Chang and S.S. Banda, “Optimal H°° norm computation for multivariable systems with multiple zeros,” IEEE-TAC, vol. AC-34, no. 5, pp. 553–557, May 1989.
B.-C. Chang, S.S. Banda, and T.E. McQuade, “Fast iterative computation of optimal two-block H°°-norm,” IEEE-TAC, vol. AC-34, no. 7, pp. 738–743, July 1989.
B.M. Chen, A. Saberi, and U.-L. Ly, “Exact computation of the infimum in H„-optimization via output feedback,” IEEE-TAC, vol. AC-37, no. 1, pp. 70–78, 1992.
B.M. Chen, A. Saberi, P. Sannuti, and Y. Shamash, “Construction and parameterization of all static and dynamic H2-optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros,” IEEE-TAC, vol. AC-38, no. 2, pp. 248–261, 1993.
G. Chen and R.J.P. de Figueiredo, “Construction of the left coprime fractional representation for a class of nonlinear control systems,” SCL, vol. 14, pp. 353–361, 1991.
C.-C. Chu, J.C. Doyle, and E.B. Lee, “The general distance problem in H„ optimal control theory,” IJC, vol. 44, no. 2, pp. 565–596, 1986.
D.F. Enns, “Model reduction with balanced realizations: An error bound and a frequency weighted generalization,” in Proc. 23rd IEEE Conf. on Decision and Contr., pp. 127–132, Dec. 1984.
C.H. Fang and F.R. Chang, “A connection between state-space and doubly coprime matrix-fraction descriptions of multivariable systems,” SCL, vol. 14, pp. 261–265, 1990.
Y.K. Foo, “Convergent inequalities for four-block ‘y-iteration in H°° optimization problems,” CTAT, vol. 6, no. 3, pp. 463–472, 1990.
T.T. Georgiou and P.P. Khargonekar, “A constructive algorithm for sensitivity optimization of periodic systems,” SIAM-JCO, vol. 25, no. 2, pp. 334–340, March 1987.
D.-W. Gu and D.Q. Mayne, “A new problem in control system design,” IEEE-TAC, vol. AC-35, no. 1, pp. 114–117, Jan. 1990.
D.-W. Gu, M.C. Tsai, and I. Postlethwaite, “Improved formulae for the 2-block H°° superoptimal solution,” Automatica, vol. 26, no. 2, pp. 437–440, 1990.
], “A frame approach to the H’” superoptimal solution,“ IEEE-TAC, vol. AC-35, no. 7, pp. 829–835, 1990.
L. Guo, L. Xia, and Y. Liu, “Recursive algorithm for the computation of the H°°-norm of polynomials,” IEEE-TAC, vol. AC-33, no. 12, pp. 1154–1158, Dec. 1988.
L. He and E. Polak, “Effective diagonalization strategies for solution of a class of optimal design problems,” IEEE-TAC, vol. AC-35, no. 3, pp. 258–267, March 1990.
J. Lam and B.D.O. Anderson, “L1 impulse response error bound for balanced truncation,” SCL, vol. 18, pp. 129–137, 1992.
Y. Liu and K.L. Teo, “Convergence rate for an approximation approach to H„-norm optimization problems with an application to controller order reduction,” Automatica, vol. 28, no. 3, pp. 617–621, 1992.
P. Pandey, C. Kenney, A. Packard, and A.J. Laub, “A gradient method for computing the optimal H„ norm,” IEEE-TAC, vol. AC-36, no. 7, pp. 887–890, 1991.
E. Polak and D.Q. Mayne, “Algorithm models for nondifferentiable optimization,” SIAM-KO, vol. 23, no. 3, pp. 477–491, May 1985.
E. Polak and S.E. Salcudean, “On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in H’” spaces,“ IEEE-TAC, vol. AC-34, no. 3, pp. 268–276, 1989.
E. Polak, S.E. Salcudean, and D.Q. Mayne, “Adaptive control of ARMA plants using worst-case design by semi-infinite optimization,” IEEE-TAC, vol. AC-32, no. 5, pp. 388–396, May 1987.
E. Polak and EJ. Wiest, “Variable-metric technique for the solution of affinely parameterized nondifferentiable optimal design problems,” JOTA, vol. 66, no. 3, pp. 391–414, 1990.
E. Polak and T.L. Wuu, “On the design of stablizing compensators via semiinfinite optimization,” IEEE-TAC, vol. AC-34, no. 2, pp. 196–200, Feb. 1989.
F. Reza, “The application of Caratheodory-Schur optimization,” Computers Elect. Engng, vol. 17, no. 1, pp. 49–53, 1991.
G. Robel, “On computing the infinity norm,” IEEE-TAC, vol. AC-34, no. 8, pp. 882–884, 1989.
U. Shaked and I. Yaesh, “A simple method for deriving J-spectral factors,” IEEE-TAC, vol. AC-37, no. 6, pp. 891–895, 1992.
K. Sugimoto and Y. Yamamoto, “A polynomial matrix method for computing stable rational doubly coprime factorization,” SCL, vol. 14, pp. 267–273, 1990.
C.P. Therapos, “Balance realization of stable transfer function matrices,” IEEE-TAC, vol. AC-37, no. 2, pp. 281–285, 1992.
RJ. Veillette and J.V. Medanic, “H„-norm bounds for ARE-based designs,” SCL, vol. 13, pp. 193–204, 1989.
C.-D. Yang and F.-B. Yeh, “A simple algorithm on minimal balanced realization for transfer function matrices,” IEEE-TAC, vol. AC-34, no. 8, pp. 879–882, 1989.
F.-B. Yeh and L.-F. Wei, “Inner-outer factorizations of right-invertible real-rational matrices,” SCL, vol. 14, pp. 31–36, 1990.
[H6] Sensitivity Considerations in Hardy Spaces Applications and Extensions
Publications in this area are pouring in and these are just representative.
T. Basar and P. Bernhard, H„—Optimal Control and Related Minimax Design Problems, a dynamic game approach. Boston: Birkhauser, 1991. Reviewed by D. Ghose, J. Indian Sciences, vol. 72, March/April 1992, and by A. Halanay and V. Ionescu, J. Rev. Romanian Sciences, Techn.-Electrotech et Energie, vol. 37, no. 2, p. 245, Bucharest 1992.
A.R. Guesalaga and H.W. Kropholler, “Improved temperature and humidity control using H m synthesis,” Proc. IEE, vol. 137, Pt. D, no. 6, pp. 374–380, 1990.
H. Kazerooni, T.-I. Tsay, and K. Hollerbach, “A controller design framework for telerobotic systems,” IEEE-TCST, vol. 1, no. 1, pp. 50–62, 1993.
M. Moran and E. Zafiriou, Robust Process Control. Englewood Cliffs, NJ: Prentice-Hall, 1989. Reviewed by J.C. Kantor, AIChE J., vol. 37, no. 12, pp. 1905–1906, 1991.
D.E. Rivera and M. Morari, “Low-order SISO controller tuning methods for the H2, H„ and 1.t objective functions,” Automatica, vol. 26, no. 2, pp. 361–369, 1990.
D.E. Rivera and M. Morari, “Plant and controller reduction problems for closed-loop performance,” IEEE-TAC, vol. AC-37, no. 3, pp. 398–404, 1992.
A. Yue and I. Postlethwaite, “Improvement of helicopter handling qualities using H’”—optimization,“ Proc. IEE, vol. 137, Pt. D, no. 3, pp. 115–129, 1990.
[I] Conference Proceedings/Reports and Book Reviews on Invariance Theory
[1] Invariance Theory and Its Use in Control Devices. Proc. First All-Union Conf. on Invariance Theory and its use in Control Systems. Moscow: Izd-vo AN SSSR, 1959. [A commentary on this meeting and its resolutions can be found in ARC vol. 20, no. 8, pp. 1109–1115, 1959.]
[2] Invariance Theory in Control Systems. Proc. Second All-Union Conf. on Invariance Theory and its use in Control Systems. Moscow: Nauka Press, 1964.
[3] Theory of Invariance of Control Systems. Proc. Third All-Union Conf. on Invariance Theory and Its Use in Control Systems. Moscow: Nauka Press, 1970.
[4] Invariance Theory and the Theory of Sensitivity of Control Systems. Materials of Fourth All-Union Conf., Parts 1–3, AN SSSR and AN Ukr SSR, 1971.
[5] News Items, Fifth All-Union Conference on Invariance Theory, Sensitivity Theory, and Their Applications. Republican School-Seminar on Invariance, Stability and Sensitivity. SAC vol. 9, pp. 73–74, Jan./Feb. 1976.
Invariance Theory, Sensitivity Theory, and Applications, Six All-Union Conference (Reports of Papers) [in Russian], Inst. of Control Problems, Moscow (1982).
Seventh All-Union Conference on the Theory of Invariance and Sensitivity of Automatic Systems (Reports of Papers) (Academician V.A. Trapeznikov, General Chairman), Baku, June 1987. [The author could not locate any other information on this and the previous entry.]
The fiftieth anniversary of publishing Professor G.V. Shchipanov’s work: “Theory and methods of design of automatic regulators,” SJAIS, vol. 22, no. 2, pp. 82–95, 1989.
N.M. Chumakov, “Fourth all-union conference on the theory of invariance and the theory of sensitivity of automatic systems,” ARC, no. 3, pp. 511–514, March 1972.
N.A. Kachanova and P.I. Chinaev, “Conference on invariance theory and its applications to automatic devices,” ARC, vol. 20, no. 8, pp. 1109–1114, Resolutions of this conference, ibid, pp. 1114–1115, Aug. 1959.
V.S. Kulebakin, Teoriia Invariantnosti i Ee Primenenie v Avtomati-Cheskikh Ustroistvakh. Moskva: 1959.
V.M. Kuntsevich, “Conclusion of discussion on the invariance of automatic control systems,” SJAIS, vol. 21, no. 2, pp. 98–99, 1988.
L.N. Mikhailov, “Some remarks on the theory of complete compensation of disturbances,” Avtomatika i Telemekhanika, no. 5, [pp. 145–154 in Russian], 1940.
T. Soveshch, Theory of Invariance and Its Application to Automatic Control [in Russian]. Izd-vo AN Uk. SSR, 1959.
M. Ulanov, “(Book Review) `The Problem of Invariance Theory In Automatic Control’,” By A.I. Kukhtenko, ARC, vol. 27, no. 4, pp. 729–731, April 1966.
S.D. Zemlyakov, “Third all-union meeting on invariance theory and its applications in automatic control systems,” ARC, no. 4, pp. 681–684, April 1967.
[J] Selected Techniques from Invariance Theory
J.K. Aggarwal, H.T. Banks, and N.H. McClamroch, “Invariance in linear systems,” JMAA, vol. 29, pp. 498–506, 1970.
S. Barnett, C. Storey, J.B. Cruz, and W.R. Perkins, “Comment on `Invariance and sensitivity’,” IEEE-TAC, vol. AC-12, pp. 210–211, April 1967.
C. Bonivento, R. Gudorzi, and G. Marro, “Parametric insensitivity and controlled invariance,” in Proc. 3rd IFAC Symp. on Sensitivity, Adaptivity and Optimality, pp. 177–182, Ischia, Italy, 1973.
V.G. Borisov, SN. Diligenskii, and A.Y. Efremov, “Synthesis of invariant control systems using eigenstructures,” ARC, vol. 51, no. 7, pp. 855–866, 1990.
L.M. Boychuk, “Necessary and sufficient conditions for absolute invariance of control systems with indirect measurement of disturbances,” SAC, vol. 2, no. 4, pp. 13–18, 1969.
L.M. Boychuk, “Was there a mistake in G.V. Shchipanov’s work?” SJAIS, vol. 19, no. 3, pp. 82–94, 1986. Comments by A.G. Ivakhnenko, ibid., pp. 95–97, and in vol. 20, no. 3, p. 87, 1987.
L.M. Boychuk, “Invariant filtering of discrete processes,” SJAIS, vol. 20, no. 2, pp. 9–15, 1987.
L.M. Boychuk and G.S. Finin, “A method of controlling objects with variable parameters based on using coordinating systems,” SJAIS, vol. 22, no. 6, pp. 37–44, 1989.
L.M. Boychuk and A.M. Voronin, “Invariance theory in control systems (a survey),” SAC, vol. 2, no. 4, pp. 1–13, 1969.
L.M. Boychuk and Y.P. Yurachkovskiy, “Static stability and homeostatism of coordinating automatic control systems,” SJAIS, vol. 23, no. 6, pp. 33–43, 1990.
J.B. Cruz, Jr., and W.R. Perkins, “On invariance and sensitivity,” in IEEE Int. Cony. Record, vol. 14, Pt. 7, pp. 159–162, 1966.
J.B. Cruz, Jr., and W.R. Perkins, “Conditions for signal and parameter invariance in dynamical systems,” IEEE- TAC, vol. AC-11, pp. 614–615, July 1966.
V.I. Elkin, “Realization, invariance, and autonomy of nonlinear controllable dynamic systems,” ARC, vol. 42, no. 7, pp. 878–885, 1981.
A.T. Fam and J.S. Meditch, “On input-output parametric invariance in linear systems,” IEEE-TAC, vol. AC-21, No. 6, pp. 870–871, Dec. 1976.
A.R. Gaiduk, “Analytic design of invariant control systems for one-dimensional plants,” ARC, vol. 42, no. 5, pp. 557–565, 1981.
A.R. Gaiduk, “Design of control systems with a given form of inputs,” ARC, vol. 45, no. 6, pp. 692–699, 1984.
A.R. Gaiduk, “Selecting the feedback in a control system of minimum complexity,” ARC, vol. 51, no. 5, pp. 593–600, 1990.
C. Gori-Giogi and O.M. Grasselli, “A new approach to the study of parameter insensitivity,” Automatica, vol. 11, pp. 181–188, 1975.
J.M. Ham, “Parameter invariance through the use of nonlinear comparators,” in Proc. Allerton Conf., pp. 578–588, 1965.
J.M. Ham and M.A. Hassan, “Appropriate parameter invariance with nonlinear feedback,” IEEE-TAC, vol. AC-10, no. 1, pp. 87–89, 1965.
A.G. Ivakhnenko and L.M. Boychuk, “Ensuring a given motion of an invariant servo system (as applied to the construction of differentiators),” SJAIS, vol. 20, no. 5, pp. 62–64, 1987.
V.I. Ivanenko, “Some questions regarding indeterminacy and dynamics in control problems,” SJAIS, vol. 20, no. 5, pp. 31–41, 1987.
C.D. Johnson, “Invariant hyperplanes for linear dynamical systems,” IEEE-TAC, vol. AC-11, pp. 113–116, Jan. 1966.
Y.S. Kan and A.I. Kibzun, “Stabilization of a dynamic system which is under the action of undetermined and random disturbances,” ARC, vol. 51, no. 12, pp. 1665–1673, 1990.
Y.S. Kharin, “Training of invariant recognition systems,” SAC, vol. 11, no. 1, pp. 17–26, 1978.
M.M. Khrustalev and M.V. Azanov, “A parametric family of generating functions and sufficient conditions for the optimality of discontinuous systems,” SJAIS, vol. 22, no. 6, pp. 78–84, 1989.
Y.R. Kotta, “Designing nonlinear discrete-time systems which are invariant under disturbances,” ARC, vol. 51, no. 3, pp. 294–300, 1990.
A.I. Kukhtenko, “Criteria for absolute invariance for control systems with variable parameters,” Izv. AN SSSR, Otd. tekhn., Energetika i Avtomatika, no. 2, 1961.
A.I. Kukhtenko, “What can the `abstract theory of systems’ offer control science?” SAC, vol. 12, no. 4, pp. 1–8, 1979.
A.I. Kukhtenko, “The basic steps in the development of invariance theory,” SAC, vol. 17, no. 2, pp. 1–10, 1984.
A.I. Kukhtenko, “Basic steps in the development of invariance theory Part 2. Extension of the sub- ject area of investigations,” SJAIS, vol. 18, no. 2, pp. 1–11, 1985.
A.I. Kukhtenko, “The basic steps in the development of invariance theory Part III. Nonlinear invariant systems,” SJAIS, vol. 18, no. 6, pp. 1–11, 1985.
R.M. Kukuliyev, “Application of invariance theory to the synthesis of inertial damped navigational systems for complex motion of an object,” SJAIS, vol. 22, no. 1, pp. 31–39, 1989.
M.B. Leitman, “Use of the invariance principle for improving the accuracy and dynamic characteristics of compensation data-measurement transducers,” ARC, vol. 39, no. 7, pp. 1077–1087, 1978.
N.N. Luzin, “Study of matrix theory of differential equations,” Avtomatika i Telemekhanika, no. 5, 1940.
N.H. McClamroch, J.K. Aggarwal, and L.G. Clark, “On parameter invariance in linear control systems,” IJC, vol. 5, no. 4, pp. 361–367, 1967.
N.H. McClamroch, J.K. Aggarwal, and L.G. Clark, “Sensitivity of linear control systems to large parameter variations,” Avtomatica, vol. 5, pp. 257–263, 1969.
V.S. Mechetnyy, “Double invariance of control systems,” SAC, vol. 2, no. 4, pp. 21–27, 1969.
V.S. Mechetnyy, “Generalized conditions for absolute invariance of horizontal flight coordinates under atmospheric disturbances,” SAC, vol. 4, no. 1, pp. 5–9, 1971.
B.G. Mel’nikov, “Sensitivity of the optimum probability filters,” ECy, vol. 23, no. 5, pp. 138–144, 1985.
A.N. Michel and V. Vittal, On the mechanism of transient instability of power systems,“ CSSP, vol. 4, no. 3, pp. 413–434, 1985.
T. Mita, “Design of a zero-sensitive systems,” IJC, vol. 24, no. 1, pp. 75–81, 1976. Comment on this and a sequence of other related papers of this author by B. Porter, ibid., vol. 27, no. 2, pp. 325–326, 1978. Author’s reply, ibid., vol. 29, no. 3, p. 535, 1979.
T. Mita and K. Hasegawa, “Zeroing and the design of a zero-sensitivity system,” EEJ, vol. 95, no. 5, pp. 118–125, Sept/Oct. 1975.
V.A. Orlov, “Technique for the analysis of invariant and optimal systems with periodic parameters,” ARC, vol. 27, no. 9, pp. 1522–1534, Sept. 1966.
T.K.C. Peng, “Invariance and stability for bounded uncertain systems,” SIAM J. Contr., vol. 10, no. 4, pp. 679–690, Nov. 1972.
B.N. Petrov, V.V. Dement’yeva, and M.M. Khrustalev, “Synthesis of an invariant dynamic system with program control,” ECy, vol. 19, no. 4, pp. 148–151, 1981.
B.N. Petrov and P.D. Krut’ko, “Sensitivity theory in automatic control,” ECy, vol. 8, no. 2, pp. 380–389, 1970.
B.N. Petrov, V.Y. Rutkovski, and I.N. Krutova, “The problems of invariance, sensitivity and optimization in the theory of one class of self-adapting systems,” Proc. IFAC, vol. 1 (of the 3rd Congress), pp. 18D. 1–18D. 10, 1966.
V.P. Pichkurenko and O.V. Fokin, “Invariance conditions in stationary and nonstationary systems,” SAC, vol. 14, no. 4, pp. 27–38, 1969.
J. Preminger and J. Rootenberg, “Some considerations relating to control systems employing the invariance principle,” IEEE-TAC, vol. AC-9, pp. 209–215, July 1964.
L.I. Rozonoer, “A variational approach to the problem of invariance of automatic control systems. I,” ARC, vol. 24, no. 6, pp. 680–691, Nov., 1963.
L.I. Rozonoer, “A variational approach to the problem of invariance II,” ARC vol. 24, no. 7, pp. 793–800, Dec. 1963. [cf., [63] and [49] for comments.]
R.S. Rutman, “Conditions of zero sensitivity in linear control systems,” ECy, vol. 7, no. 2, pp. 137–145, March/April 1969.
R.S. Rutman and M.S. Epelman, “Parametric invariance of linear dynamic systems,” Dokl. Adad. Nauk. USSR, vol. 159, no. 4, pp. 764–766, 1964.
B.A. Ryabov and G.P. Sachkov, “Estimating the value of E-invariant systems,” SJAIS, vol. 23, no. 4, pp. 23–30, 1990.
P.H. Shac, “Invariance and controllability in certain linear processes,” ARC vol. 37, no. 7, pp. 994–1003, 1976. [The author of this paper seems to be the same as the next one.]
F.H. Shak, “Invariance in linear discrete processes,” ARC, vol. 34, no. 6, pp. 991–976, June 1973.
G.V. Shchipanov, “Theory and methods of design of control systems,” Avtomatika i Telemekhanika no. 1, 1939. [This entry which has been cited (with a minor variation) in a number of papers in this area is included here only for historical reasons. The actual paper has been recently reappeared, with perhaps a more accurate tide than the earlier translation, in [I. 8].]
Y.B. Shtessel and A.Y. Evnin, “Invariant control of output of nonlinear systems,” ARC, vol. 51, no. 3, pp. 315–323, 1990.
E.M. Solnechnyi, “Making the dynamic properties of a single-channel control system approach absolute invariance,” ARC, vol. 46, no. 4, pp. 449–456, 1985.
E.M. Solnechnyy, “Investigation of the stability of a Shchipanov system of intentionally introduced small stabilizing inertialities,” LIAIS, vol. 20, no. 6, pp. 79–83, 1987.
E.M. Solnechnyi, “Conditions of stability and robustness of a single-channel invariant system of any order,” ARC, vol. 49, no. 7, pp. 864–873, 1988.
R.O. Spas’kyy, “Absolute invariance conditions for nonlinear systems of differential equations,” SAC, vol. 14, no. 4, pp. 39–44, 1969.
A.F. Starikov, “Invariance in linear systems,” ECy, vol. 23, no. 2, pp. 131–133, 1985.
A.V. Ushakov, “Conditions of zero parametric sensitivity in the tracking problem,” ARC, vol. 42, no. 9, pp. 1157–1163, Sept. 1981.
A.V. Ushakov and A.A. Dzhamanbaev, “A geometrical approach in the problem of finding a class of regulators that ensure zero parametric sensitivity,” SJAIS vol. 20, no. 5, pp. 84-, 1987. [The author regretfully could not locate the rest of this article, it has been apparently deleted in the course of production.]
V.A. Utkin and V.I. Utkin, “Design of invariant systems by the method of separation of motions,” ARC, vol. 44, no. 12, pp. 1559–1566, Dec. 1983.
V.V. Velichenko, “The variational method in invariance theory,” SAC, vol. 5, no. 3, pp. 1–16, May/June 1972.
V.V. Velichenko, “Invariance of discontinuous systems,” ARC, no. 8, pp. 1336–1341, Aug. 1973.
A.M. Voronin, “Structural analysis of a class of invariant control systems,” SAC, vol. 3, no. 4, pp. 8–10, 1970.
M. Vukobratovic, “Invariance and sensitivity of multivariate dynamic systems,” SAC, vol. 13, no. 4, pp. 1–7, 1968.
P.KC. Wang, “Invariance, uncontrollability, and unobservability in dynamical systems,” IEEE-TAC, vol. AC-10, pp. 366–367, July 1965.
S.V. Yemel’yanov, S.K. Korovin, and B.V. Ulanov, “Control of nonstationary dynamic systems with coordinate-parametric feedback,” ECy, vol. 20, no. 6, pp. 120–130, 1982.
[K] Bounded Uncertainty and Disturbance Rejection [K1] Bounded Uncertainty
M.A. Aizerman and Y.S. Pyatnitskiy, “Theory of dynamic systems which incorporate elements with incomplete information and its relation to the theory of discontinuous systems,” JFI, vol. 306, no. 6, pp. 379–408, 1978.
Y.I. Alimov, “On the application of Lyapunov’s direct method to differential equations with ambiguous right sides,” ARC, vol. 22, no. 7, pp. 713–725, July 1961.
G.M. Bairn and V.T. Strashko, “A minimax approach to static plant control with incomplete information,” SAC, vol. 11, no. 5, pp. 1–6, 1978.
G.M. Bairn and V.T. Strashko, “Minimax control of multivalued controlled processes,” SAC, vol. 12, no. 3, pp. 46–55, 1979.
EA. Barbashin, “On the theory of generalized dynamical systems,” Uch. Zap. Moskov. Gosudarst. Univ. no. 135, 1949, pp. 110–133.
B.R. Barmish, “Robust solution of perturbed dynamical equations from within a convex restraint set,” IEEE-TAC, vol. AC-24, no. 6, pp. 921–926, 1979.
B.R. Barmish, “Stabilization of uncertain systems via linear control,” IEEE-TAC, vol. AC-28, no. 8, pp. 848–850, Aug. 1983.
B.R. Barmish, “Necessary and sufficient conditions for quadratic stablizability of an uncertain system,” JOTA, vol. 46, no. 4, pp. 399–408, 1985.
B.R. Barmish, L.E. Blume, and S.D. Chikte, “Robustness of systems with uncertainties in the input,” JMAA, vol. 84, pp. 208–234, 1981.
B.R. Barmish, M. Corless, and G. Leitmann, “A new class of stabilizing controllers for uncertain dynamical systems,” SIAM-JCO, vol. 21, no. 2, pp. 246–255, March 1983.
B.R. Barmish and G. Leitmann, “On ultimate boundedness control of uncertain systems in the absence of matching assumptions,” IEEE-TAC, vol. AC-27, no. 1, pp. 153–158, Feb. 1982.
B.R. Barmish, W.E. Schmitendorf, and G. Leitmann, “A note on avoidance control,” ASMEJDSMC, vol. 103, pp. 69–70, March 1981.
G. Basile and G. Marro, “On the robust controlled invariant,” SCL, vol. 9, pp. 191–195, 1987.
A.S. Belen’kii, “Min-max problems with monotone functions on polyhedral sets,” ARC, vol. 43, no. 10, pp. 1304–1314, Oct. 1982.
A.S. Belen’kii, “Search for min-max of two monotone functions in polyhedral set,” ARC, vol. 43, no. 11, pp. 1389–1393, Nov. 1982.
J. Bernussou, P.L.D. Peres, and J.C. Geromel, “A linear programming oriented procedure for quadratic stabilization of uncertain systems,” SCL, vol. 13, pp. 65–72, 1989.
V.N. Bukov, “Optimal algorithms in problems with bounded controllable coordinates,” ECy, vol. 20, no. 2, pp. 133–140, 1982.
C.H. Chao and H.L. Stafford, “On the robustness of linear stabilizing feedback control for linear uncertain systems: Multi-input case,” JOTA, vol. 64, no. 2, pp. 229–244, 1990.
C.H. Chao and H.L. Stafford, “Necessary and sufficient condition in Lyapunov robust control: Multi-input case,” JOTA, vol. 66, no. 1, pp. 1–21, 1990.
Y.H. Chen, “Robust output feedback controller. Direct design,” IJC, vol. 46, no. 3, pp. 10831091, 1987.
Y.H. Chen, “Robust output feedback controller: Indirect design,” IJC, vol. 46, no. 3, pp. 1093–1103, 1987.
Y.H. Chen, “On the robustness of mismatched uncertain dynamical systems,” ASME-JDSMC, vol. 109, pp. 29–35, 1987.
Y.H. Chen, “Design of robust controllers for uncertain dynamical systems,” IEEE-TAC, vol. AC-33, no. 5, pp. 487–491, May 1988.
Y.H. Chen and G. Leitmann, “Robustness of uncertain systems in the absence of matching assumptions,” IJC, vol. 45, no. 5, pp. 1527–1542, 1987.
M.J. Corless and G. Leitmann, “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,” IEEE-TAC, vol. AC-26, no. 5, pp. 1139–1144, Oct. 1981. Erratum, ibid., vol. AC-28, no. 2, p. 249, Feb. 1983.
M.J. Corless and G. Leitmann, “Controller design for uncertain systems via Lyapunov function,” in Proc. Ameri-
can Contr. Conf. pp. 2019–2025, 1988.
A.F. Filippov, “Differential equations with many-valued discontinuous right-hand side,” Soviet Mathematics, vol. 4, no. 4, pp. 941–945, 1963.
], Differential Equations with Discontinuous Righthand Sides. Dordrecht, the Neth- erlands: Kluwer, 1988. Reviewed by S.R. Bernfeld, SIAM R., vol. 32, no. 2, pp. 312–315, 1990.
A.R. Galimidi and B.R. Barmish, “The constrained Lyapunov problem and its application to robust output feedback stabilization,” IEEE-TAC, vol. AC-31, pp. 410–419, May 1986.
F. Garofalo and G. Leitmann, “Guaranteeing ultimate boundedness and exponential rate of convergence for a class of nominally linear uncertain systems,” ASME-JDSMC, vol. 111, pp. 584–588, Dec. 1989.
D.P. Goodall and E.P. Ryan, “Feedback controlled differential inclusions and stabilization of uncertain dynamical systems,” SIAM-JCO, vol. 26, no. 6, pp. 1431–1441, 1988.
G. Gu, “Stabilizability conditions of multivariable uncertain systems via output feedback control,” IEEE-TAC, vol. AC-35, no. 8, pp. 925–927, Aug. 1990.
S. Gutman, “Uncertain dynamical systems - A Lyapunov min-max approach,” IEEE-TAC, vol. AC-24, no. 3, pp. 437–443, June 1979. Correction, ibid., vol. AC-25, no. 3, p. 613, June 1980.
S. Gutman, “Synthesis of min-max strategies,” JOTA, vol. 46, no. 4, pp. 515–523, 1985.
I.-J. Ha, “New matching conditions for output regulation of a class of uncertain nonlinear systems,” IEEE-TAC, vol. AC-34, no. 1, pp. 116–119, Jan. 1989.
T.H. Hopp and W.E. Schmitendorf, “Design of a linear controller for robust tracking and model following,” ASME-JDSMC, vol. 112, pp. 552–558, Dec. 1990.
F. Jabbari and W.E. Schmitendorf, “Effects of using observers on stabilization of uncertain linear systems,” IEEE-TAC, vol. AC-38, no. 2, pp. 266–271, 1993.
K. Khorasani, “Robust stabilization of non-linear systems with unmodelled dynamics,” IJC, vol. 50, no. 3, pp. 827–844, 1989.
N.F. Kirichenko, “Minimax control and estimation in dynamic systems,” SAC, vol. 15, no. 1, pp. 31–39, 1982.
N.A. Lehtomaki, D.A. Castanon, B.C. Levy, G. Stein, N.R. Sandell, Jr., and M. Athans, “Robustness and modeling error characterization,” IEEE-TAC, vol. AC-29, no. 3, pp. 211–220, March 1984.
G. Leitmann, “Guaranteed ultimate boundedness for a class of uncertain linear dynamical systems,” IEEE-TAC, vol. AC-23, no. 6, pp. 1109–1110, Dec. 1978.
G. Leitmann, “Guaranteed asymptotic stability for a class of uncertain linear dynamical sys- tems,” JOTA, vol. 27, no. 1, pp. 99–106, 1979.
G. Leitmann, “Guaranteed asymptotic stability for some linear systems with bounded uncertain- ties,” ASME-JDSMC, vol. 101, pp. 212–216, Sept. 1979.
], “On the efficacy of nonlinear control in uncertain linear systems,” ASME-JDSMC, vol. 102, pp. 95–102, 1981.
G. Leitmann, E.P. Ryan, and A. Steinberg, “Feedback control of uncertain systems: Robustness with respect to neglected actuator and sensor dynamics,” IJC, vol. 43, no. 4, pp. 12431256, 1986.
T.-L. Liao, L.-C. Fu, and C.-F. Hsu, “Output tracking control of nonlinear systems with mismatched uncertainties,” SCL, vol. 18, pp. 39–47, 1992.
A. Linnemann, I. Postlethwaite, and B.D.O. Anderson, “Almost disturbance decoupling with stabilization by measurement feedback,” SCL, vol. 12, pp. 225–234, 1989.
A. Marchand, “Sur les champs de demi-droites et les equations differentielles du premier ordre,” Bulletin de la Societe Mathematique de France, vol. 62, pp. 1–38, 1934.
A. Marchand,, “Sur les champs continus de demi-cones convexes’ et leurs integrales,” Compositio Mathematica, vol. 3, pp. 89–127, 1936.
P. Myszkorowski, “Practical stabilization of a class of uncertain nonlinear systems,” SCL, vol. 18, pp. 233–236, 1992.
I.R. Petersen, “Structural stabilization of uncertain systems: Necessity of the matching condition,” SIAM-JCO, vol. 23, no. 2, pp. 286–296, March 1985.
S. Phoojaruenchanachai and K. Furuta, “Memoryless stabilization of uncertain linear systems including time-varying state delays,” IEEE-TAC, vol. AC-37, no. 7, pp. 1022–1026, 1992.
Z. Qu, “Robust control of a class of nonlinear uncertain systems,” IEEE-TAC, vol. AC-37, no. 9, pp. 1437–1442, 1992.
Z. Qu, “Global stabilization of nonlinear systems with a class of unmatched uncertain- ties,” SCL, vol. 18, pp. 301–307, 1992.
M.A. Rotea and P.P. Khargonekar, “Stabilization of uncertain systems with norm bounded uncertainty - A control Lyapunov function approach,” SIAM-JCO, vol. 27, no. 6, pp. 14621476, 1989.
E. Roxin, “Stability in general control systems,” JDE, vol. 1, no. 2, pp. 115–150, 1965.
E. Roxin, “On generalized dynamical systems defined by contingent equations,” JDE, vol. 1, no. 2, pp. 188–205, 1965.
E. Roxin, “On asymptotic stability in control systems,” Rendiconti del Circolo Matematico, di Palermo, series II, vol. XV, pp. 193–208, 1966.
W.E. Schmitendorf, “Stability controllers for uncertain linear systems with additive disturbances,” IJC, vol. 47, no. 1, pp. 85–95, 1988.
W.E. Schmitendorf and B.R. Barmish, “Null controllability of linear systems with constrained controls,” SIAM-JCO, vol. 18, no. 4, pp. 327–345, 1980.
J.-C. Shen, B.-S. Chen, and F.-C. Kung, “Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach,” IEEE-TAC, vol. AC-36, no. 5, pp. 638–640, 1991.
S.N. Singh, “Ultimate boundedness control of uncertain robotic systems,” IJSS, vol. 17, no. 6, pp. 859–863, 1986.
H.L. Stafford and C.H. Chao, “A necessary and sufficient condition in Lyapunov robust control,” JOTA, vol. 63, no. 2, pp. 191–203, 1989.
H.L. Stafford and C.H. Chao, “On the robustness of linear stabilizing feedback control for linear uncertain sys- tems,” JOTA, vol. 63, no. 2, pp. 205–212, 1989.
J.S. Thorp and B.R. Barmish, “On guaranteed stability of uncertain linear systems via linear control,” JOTA, vol. 35, no. 4, pp. 559–579, 1981.
A. Trofino Neto, J.M. Dion, and L. Dugard, “Robustness bounds for LQ regulators,” IEEE-TAC, vol. AC-37, no. 9, pp. 1373–1377, 1992.
A. Trofino Neto, J.M. Dion, and L. Dugard, “On the robustness of LQ regulators for discrete-time systems,” IEEE-TAC, vol. AC-37, no. 10, pp. 1564–1568, 1992.
S.-C. Tsay, “Robust control for linear uncertain systems via linear quadratic state feedback,” SCL, vol. 15, pp. 199–205, 1990.
D.J. Wilson and G. Leitmann, “Minimax control of systems with uncertain state measurements,” AMO, vol. 2, no. 4, pp. 315–336, 1976.
S.C. Zaremba, “Sur les equations au paratingent,” Bulletin des Sciences Mathematiques, (2nd series), vol. 60, pp. 139–160, 1936.
[K] Bounded Uncertainty and Disturbance Rejection [K2] Disturbance Rejection
T. Basar, “A dynamic games approach to controller design: Disturbance rejection in discrete-time,” IEEE-TAC, vol. AC-36, no. 8, pp. 936–952, 1991.
S.P. Bhattacharyya, A.C. del Nero Gomes, and J.W. Howze, “The structure of robust disturbance rejection control,” IEEE-TAC, vol. AC-28, no. 9, pp. 874–881, Sept. 1983.
B.C. Chang and J.B. Pearson, Jr., “Optimal disturbance reduction in linear multivariable systems,” IEEE-TAC, vol. AC-29, pp. 880–887, Oct. 1984.
H. Chapellat and M. Dahleh, “Analysis of time-varying control strategies for optimal disturbance rejection and robustness,” IEEE-TAC, vol. AC-37, no. 11, pp. 1734–1745, 1992.
C.-M. Chien and B.-C. Wang, “An SISO uncertain system designed by an equivalent disturbance attenuation method,” CTAT, vol. 6, no. 2, pp. 257–271, 1990.
C. Commault, J.-M. Dion, and A. Perez, “Disturbance rejection for structured systems,” IEEE-TAC, vol. AC-36, no. 7, pp. 884–887, 1991.
M.A. Dahleh and J.B. Pearson, Jr., 1 1 -Optimal feedback controllers for MIMO discrete-time systems,“ IEEE-TAC, vol. AC-32, pp. 314–322, April 1987.
M.A. Dahleh and J.B. Pearson, “Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization,” IEEE-TAC, vol. AC-33, no. 8, pp. 722–731, Aug. 1988. Comments, with reply, by J. Wu, IL-J. Fang, J.-Y. Li, and J.-J. Chen, ibid., vol. AC-38, no. 5, p. 831, 1993.
M.A. Dahleh and J.S. Shamma, “Rejection of persistent bounded disturbances: Nonlinear controllers,” SCL, vol. 18, pp. 245–252, 1992.
M.A. Dahleh, P.G. Voulgaris, and L.S. Valavani, “Optimal and robust controllers for periodic and multirate systems,” IEEE-TAC, vol. AC-37, no. 1, pp. 90–99, 1992.
R.J. de Figueiredo and G. Chen, “Optimal disturbance rejection for nonlinear control systems,” IEEE-TAC, vol. AC-34, no. 12, pp. 1242–1248, Dec. 1989.
G. Deodhare and M. Vidyasagar, “Every stabilizing controller is 11-and H„-optimal,” IEEE-TAC, vol. AC-36, no. 9, pp. 1070–1073, 1991.
M. Fujita, K. Uchida, and F. Matsumura, “Asymptotic H°° disturbance attenuation based on perfect observation,” IEEE-TAC, vol. AC-36, no. 7, pp. 875–880, 1991.
O.M. Grasselli and S. Longhi, “Robust output regulation under uncertainties of physical parameters,” SCL, vol. 16, pp. 33–40, 1991.
A. Isidori and A. Astolfi, “Disturbance attenuation and H„-control via measurement feedback in nonlinear systems,” IEEE-TAC, vol. AC-37, no. 9, pp. 1283–1293, 1992.
M.H. Khammash, “Necessary and sufficient conditions for the robustness of time-varying systems with applications to sampled-data systems,” IEEE-TAC, vol. AC-38, no. 1, pp. 49–57, 1993.
E. Noldus, “Disturbance rejection using dynamic output feedback,” Proc. IEE, vol. 129, Pt. D, no. 3, pp. 76–80, May. 1982.
H. Ozbay, “On L1 optimal control,” IEEE-TAC, vol. AC-34, pp. 884–885, Aug. 1989.
P.N. Paraskevopoulos, F.N. Koumboulis, and K.G. Tzierakis, “Disturbance rejection of left-invertible systems,” Automatica, vol. 28, no. 2, pp. 427–430, 1992.
A.G. Parlos, A.F. Henry, F.C. Schweppe, L.A. Gould, and D.D. Lanning, “Nonlinear multivariable control of nuclear power plants based on the unknown-but-bounded disturbance model,” IEEE-TAC, vol. AC-33, no. 2, pp. 130–137, 1988.
J.B. Pearson and B. Bamieh, “On minimizing maximum errors,” IEEE-TAC, vol. AC-35, no. 5, pp. 598–601, May 1990.
W.A. Porter, “Concerning disturbance measures in linear systems,” IEEE-TAC, vol. AC-11, pp. 532–534, July 1966.
I. Rhee and J.L. Speyer, “A game theoretic approach to a finite-time disturbance attenuation problem,” IEEE-TAC, vol. AC-36, no. 9, pp. 1021–1032, 1991.
J.S. Shamma, “Performance limitations in sensitivity reduction for nonlinear plants,” SCL, vol. 17, pp. 43–47, 1991.
J.S. Shamma and M. Athans, “Guaranteed properties of gain scheduled control for linear parameter-varying plants,” Automafica, vol. 27, no. 3, pp. 559–564, 1991.
J.S. Shamma and MA. Dahleh, “Time-varying versus time-invariant compensation for rejection of persistent bounded disturbances and robust stabilization,” IEEE-TAC, vol. AC-36, no. 7, pp. 838–847, 1991.
N. Sivashankar and P.P. Khargonekar, “Robust stability and performance analysis of sampled-data systems,” IEEE-TAC, vol. AC-38, no. 1, pp. 58–69, 1993.
R.E. Skelton and G. Zhu, “Optimal L„ bounds for disturbance robustness,” IEEE-TAC, vol. AC-37, no. 10, pp. 1568–1572, 1992.
A.A. Stoorvogel and J.W. van der Woude, “The disturbance decoupling problem with measurement feedback and stability for systems with direct feedthrough matrices,” SCL, vol. 17, pp. 217–226, 1991.
K.C.Q. Tsai, D.M. Auslander, “A statistical methodology of designing controllers for minimum sensitivity of parameter variations,” ASME-JDSMC, vol. 110, pp. 126–133, June 1988.
P.B. Usoro, F.C. Schweppe, D.N. Wormley, and L.A. Gould, “Ellipsoidal set-theoretic control synthesis,” ASME-JDSMC, vol. 104, pp. 331–336, Dec. 1982.
M. Vidyasagar, “Optimal rejection of persistent bounded disturbances,” IEEE-TAC, vol. AC-31, no. 6, pp. 527–534, June 1986.
M. Vidyasagar, “Further results on the optimal rejection of persistent bounded disturbances,” IEEE-TAC, vol. AC-36, no. 6, pp. 642–652, 1991.
S. Weiland and J.C. Willems, “Almost disturbance decoupling with internal stability,” IEEE-TAC, vol. AC-34, no. 3, pp. 277–286, March 1989.
G. Zhu and R.E. Skelton, “Robust discrete controllers guaranteeing 12 and 1.. performances,” IEEE-TAC, vol. AC-37, no. 10, pp. 1620–1625, 1992.
[L] Sensitivity Analyses in Nonlinear, Time-Varying Systems, System Sensitivity Theory - Statistically Oriented, Certain Statistical Problems, and Certain Social and Economical Matters
B.D.O. Anderson and J.B. Moore, “Tolerance of nonlinearities in time-varying optimal systems,” Elect. Lea., vol. 3, no. 6, pp. 250–251, June 1967.
D.P. Atherton, H.T. Dorrah, and S.T. Nichols, “The algebra of X. matrices: An effective tool for sensitivity analysis,” IEEE-TAC, vol. AC-21, no. 6, pp. 881–882, 1976.
O. Berman, E. Modiano, and JA. Schnabel, “Sensitivity analysis and robust regression in investment performance evaluation,” IJSS, vol. 15, no. 5, pp. 481–489, 1984.
X.-R. Cao and Y.-C. Ho, “Sensitivity analysis and optimization of throughput in a production line with blocking,” IEEE-TAC, vol. AC-32, no. 11, pp. 959–967, Nov. 1987.
X.-R. Cao and Y.-C. Ho, “Estimating the sojourn time sensitivity in queueing networks using perturbation analysis,” JOTA, vol. 53, no. 3, pp. 353–375, 1987.
C.G. Cassandras and S.G. Strickland, “On-line sensitivity analysis of Markov chains,” IEEE-TAC, vol. AC-34, no. 1, pp. 76–86, Jan. 1989.
C.G. Cassandras and S.G. Strickland, “Observable augmented systems for sensitivity analysis of Markov and semi- Markov processes,” IEEE-TAC, vol. AC-34, no. 10, pp. 1026–1037, Oct. 1989.
P.I. Dekhtyarenko and A.Z. Zakharyan, “Effect of parameter deviations of nonlinear loops on equivalent transfer function,” SAC, vol. 6, pp. 5–12, Nov./Dec. 1973.
R.M. DeSantis and W.A. Porter, “A generalized Nyquist plot and its use in sensitivity analysis,” IJSS, vol. 5, no. 12, pp. 1143–1153, 1974.
D. Efthymiatos and S. Tzafestas, “A generalized sensitivity approach to feedback systems in Hilbert space,” IJSS, vol. 4, no. 1, pp. 87–95, 1973.
D.L. Erickson and F.E. Norton, “Application of sensitivity constrained optimal control to national economic policy formulation,” in Control and Dynamic Systems advances in theory and applications, vol. 9 (C.T. Leondes, Ed.). New York Academic Press, pp. 131–237, 1973.
M.A. Eyler, “Sensitivity of sample values to parameter changes,” JOTA, vol. 45, no. 1, pp. 159–163, 1985.
A. Feintuch, P.P. Khargonekar, and A. Tannenbaum, “On the sensitivity minimization problem for linear time-varying periodic systems,” SIAM-JCO, voL 24, no. 5, pp. 1076–1085, 1986.
I.V. Filatov and S.N. Sharov, “An investigation of parametric sensitivity of nonlinear dynamic correcting devices,” ECy, vol. 15, pp. 166–169, 1977.
A. Ford and P. Gardiner, “A new measure of sensitivity for social system simulation models,” IEEE-TSMC, vol. SMC-9, no. 3, pp. 105–114, 1979.
J.S. Gibson and L.G. Clark, “Sensitivity analysis for a class of evolution equations,” JMAA, voL 58, pp. 22–31, 1977.
W.-B. Gong, C.G. Cassandras, and J. Pan, “Perturbation analysis of a multiclass queueing system with admission control,” IEEE-TAC, vol. AC-36, no. 6, pp. 707–723, 1991.
D.A. Hanson, W.R. Perkins, and J.B. Cruz, Jr., “Public investment strategies for regional development: An analysis based on optimization and sensitivity results,” IEEE-TSMC, vol. SMC-6, no. 3, pp. 165–176, March 1976.
R.J. Herbert, “Structural sensitivity of feedback controls for second-order nonlinear systems,” JOTA, vol. 30, no. 3, pp. 395–421, 1980.
Y.-C. Ho, “Parametric sensitivity of a statistical experiment,” IEEE-TAC, vol. AC-24, no. 6, pp. 982–983, Dec. 1979.
J.M. Holtzman, “On using perturbation analysis to do sensitivity analysis: Derivatives versus differences,” IEEE-TAC, vol. AC-37, no. 2, pp. 243–247, 1992.
Y.B. Kadimov, E.Y. Kuliyev, and S.I. Myachin, “Some questions concerning the application of the sensitivity theory to an analysis of transient processes while simulating systems with distributed parameters on analog computers,” Proc. IFAC, voL 3 (of the 5th Congress), pp. 31.4.1–31. 4. 9, 1972.
V. Kaitala and G. Leitmann, “Stabilizing employment in a fluctuating resource economy,” JOTA, vol. 67, no. 1, pp. 1–16, 1990.
K.-I. Kanatani, “Generalized global sensitivity and correlation analysis,” IC, vol. 47, pp. 3758, 1980.
Y.S. Kharin, “Robustness of decision rules in the presence of errors of classification of the training sample,” ARC, vol. 44, no. 11, pp. 1470–1479, Nov. 1983.
D.G. Lainiotis and F.L. Sims, “Sensitivity analysis of discrete Kalman filters,” IJC, vol. 12, no. 4, pp. 657–669, 1970.
D.H. Martin, “Prediction sensitivity to functional perturbations in modelling with ordinary differential equations,” AMO, vol. 6, pp. 123–137, 1980.
N.H. McClamroch, “Evaluation of suboptimality and sensitivity in control and filtering processes,” IEEE-TAC, vol. AC-14, pp. 282–285, June 1969.
L.H. Meyer, F.Q. Raines, T.J. Tarn, and S.K. Gupta, “Optimal coordination of aggregate stabilization policy and price controls: A sensitivity analysis,” Proc. IFAC, vol. 3 (of the 6rd Congress), pp. 62.4.1–62. 4. 8, 1975.
K.S. Miller and F.J. Murray, “A. mathematical basis for an error analysis of differential analyzers,” JMP, vol. 32, nos. 2 and 3, pp. 136–163, July/Oct. 1953.
R.W. Newcomb and B.D.O. Anderson, “A distributional approach to time-varying sensitivity,” SIAM-JAM, vol. 15, no. 4, pp. 1001–1010, 1967.
W.R. Perkins and J.B. Cruz, Jr., “Sensitivity operator for linear time-varying systems,” in Sensitivity Methods in Control Theory (L. Radanovic, Ed.). New York: Pergamon Press 1966. (Proc. Int. Symp. Dubrovink, Aug. 1964.)
W.A. Porter, “Some theoretical limitations of system sensitivity reduction,” in Proc. Allerton Conf., pp. 241–251, 1965.
W.A. Porter and R.M. DeSantis, “Sensitivity analysis in multilinear systems,” IJSS, vol. 7, no. 2, pp. 191–205, 1976.
J. Rootenberg and P. Courtin, “Sensitivity of optimal control systems with bang-bang control,” IJC, vol. 18, no. 3, pp. 537–543, 1973.
A.P. Sage, “Sensitivity analysis in systems for planning and decision support,” JFI, vol. 312, nos. 3 /4, pp. 265–291, Sept./Oct. 1981.
F.R. Shupp, “Financing fiscal policy: A sensitivity analysis,” JFI, vol. 312, nos. 3/4, pp. 293306, Sept./Oct. 1981.
A.A. Siapkara, “Human operator system representation via cross-sensitivity minimization,” JFI, vol. 312, nos. 3/4, pp. 307–326, 1981.
L.H. Sibul, “Sensitivity analysis of linear control systems with random plant parameters,” IEEE-TAC, vol. AC-15, pp. 459–462, Aug. 1970.
P. Stavroulakis and P.E. Sarachik, “Low sensitivity feedback gains for deterministic and stochastic control systems,” IJC, vol. 19, no. 1, pp. 15–31, 1974.
N. Sundararajan and J.B. Cruz, Jr., “Policy modification for macro-economic systems resulting in reduced sensitivity to parameter perturbations,” IJSS, vol. 5, no. 12, pp. 1193–1205, 1974.
S.G. Tzafestas, “Sensitivity in the decoupling of non-linear control systems,” IJC, vol. 18, no. 6, pp. 1249–1266, 1973.
M. Vukobratovic, “Note on the sensitivity of non-linear dynamic systems,” IEEE-TAC, vol. AC-13, pp. 453–454, Aug. 1968.
M. Vukobratovic and D. Juricic, “Sensitivity of nonlinear systems,” ARC, no. 9, pp. 13811388, Sept. 1970.
J. Yang and HJ. Kushner, “A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems,” SIAM-JCO, vol. 29, no. 5, pp. 1216–1249, 1991.
G.E. Young and D.M. Auslander, “A design methodology for nonlinear systems containing parameter uncertainty,” ASME-JDSMC, vol. 106, pp. 15–20, March 1984.
K.-K. D. Young, “Near insensitivity of linear feedback systems,” JFI, vol. 314, no. 2, pp. 129–142, Aug. 1982.
A.V. Yudayev, A.M. Lisitsyn, and N.P. Baranov, “Optimization of controllers with respect to minimum sensitivity to disturbances,” ECy, vol. 13, no. 1, pp. 141–145, 1975.
[M] Sensitivity Considerations in Nonlinear Systems
J.L. Aravena and W.A. Porter, “Finite memory partial inverses,” IEEE-TCAS, vol. CAS-28, pp. 287–294, April 1981.
J.L. Aravena and W.A. Porter, “System partial inverses for sensitivity, adaptivity and estimation,” JFI, vol. 312, nos. 3 /4, pp. 141–165, Sept/Oct 1981.
J.B. Cruz, D.P. Looze, and W.R. Perkins, “Sensitivity analysis of nonlinear feedback systems,” JFI, vol. 312, nos. 3 /4, pp. 199–215, Sept/Oct. 1981.
S.A. Doganovskii, “Compensation of perturbations in nonlinear systems,” ARC, vol. 23, no. 6, pp. 676–690, Dec. 1962.
O.N. Fomenko, “Accuracy of nonlinear control systems with random parameters,” ECy, vol. 5, no. 1, pp. 131–138, Jan./Feb., 1967.
W. Hejmo, “Sensitivity to switching-function variations in a time-optimal positional system,” IJC, vol. 39, no. 1, pp. 19–30, 1984.
E. Kreindler, “On the closed-loop sensitivity reduction of non-linear systems,” IJC, vol. 6, no. 2, pp. 171–178, 1967.
E. Kreindler, “On sensitivity of closed-loop nonlinear optimal control systems,” SIAM J. Contr. vol. 7, no. 3, pp. 512–520, Aug. 1969.
E. Kreindler, “Sensitivity of time-varying linear optimal control systems,” JOTA, vol. 3, no. 2, pp. 98–106, 1969.
V.A. Mayorov, Y.G. Borisenko, O.B. Kerber, V.V. Pavlov, and O.S. Yakovlev, “The problem of synthesizing a nonlinear control law,” SJAIS, vol. 21, no. 2, pp. 41–49, 1988.
K. Pedersen and L. Nardizzi, “Synthesis of optimally sensitive control for systems with time-varying parameters,” IJC, vol 15, no. 1, pp. 1–20, 1972.
W.A. Porter, “Minimizing system sensitivity through feedback,” JFI, vol. 286, pp. 225–240, 1968.
W.A. Porter, “On sensitivity in multivariable non-stationary systems,” IJC, vol. 7, pp. 481–491, 1968.
W.A. Porter, “The Interrelationship between observers and system sensitivity,” IEEE-TAC, vol. AC-22, no. 2, pp. 144–146, Feb. 1977.
W.A. Porter, “Partial inverses for parameter sensitivity reduction,” ITC, vol. 29, no. 6, pp. 949–961, 1979.
S.S. Rao, T.-S. Pan, and V.B. Venkayya, “Robustness improvement of actively controlled structures through structural modifications,” AIAA J., vol. 28. no. 2, pp. 353–361, Feb. 1990.
N. Sundararajan and J.B. Cruz, Jr., “Sensitivity reduction in time-varying linear and nonlinear systems,” IJC, vol. 15, no. 5, pp. 937–943, 1972.
V.D. Tourassis and C.P. Neuman, “Robust nonlinear feedback control for robotic manipulators,” Proc. IEE, vol. 132, Pt. D, no. 4, pp. 134–143, July 1985.
[N] Sensitivity Considerations in Discrete-Time (Digital) Systems Sensitivity Reduction of Systems with Time Lag, and Multi-Dimensional Digital Systems
S. Barnett, “Insensitivity of optimal linear discrete-time regulators,” IJC, vol. 21, no. 5, pp. 843–848, 1975.
A.W. Bennett and A.P. Sage, “Discrete system sensitivity and variable increment sampling,” in Proc. Joint Auto. Contr. Conf., pp. 603–612, 1967.
G.A. Bekey and R. Tomovic, “Sensitivity of discrete systems to variation of sampling interval,” IEEE-TAC, vol. AC-11, no. 2, pp. 284–287, April 1966.
K.C. Cheok, N.K. Loh, and M.A. Zohdy, “Cost sensitivity analysis for discrete-time optimal feedback controllers with time-multiplied performance indexes,” IEEE-TAC, vol. AC-31, no. 3, pp. 262–263, March 1986.
S.-M. Chiang and Y.-P. Shih, “Low sensitivity feedback control of non-linear discrete systems,” IJC, vol 14, no. 4, pp. 659–668, 1971.
S.-M. Chiang and Y.-P. Shih, “Low-sensitivity design of optimal linear control systems with transportation lag,” Proc. IEE, vol. 120, no. 7, pp. 810–813, July 1973.
F.H. Clarke and P.R. Wolenski, “The sensitivity of optimal control problems to time delay,” SIAM-JCO, vol. 29, no. 5, pp. 1176–1215, 1991.
M.A. Connor, “Minimization of performance sensitivity for time-lag systems,” IEEE-TAC, vol. AC-16, no. 5, pp. 496–497, Oct. 1971.
J.B. Cruz, Jr., “Sensitivity considerations for time-varying sampled-data feedback systems,” IRE-TAC, vol. AC-6, no. 2, pp. 228–236, 1961.
J.B. Cruz, Jr., and M.E. Sawan, “Low-sensitivity optimal feedback control for linear discrete-time systems,” IEEE-TAC, vol. AC-24, no. 1, pp. 119–122, Feb. 1979.
M.A. Dahleh and J.B. Pearson, Jr., “11-Optimal feedback controllers for MIMO discrete-time systems,” IEEE-TAC, vol. AC-32, no. 4, pp. 314–322, April 1987.
C. Foias, A. Tannenbaum, and G. Zames, “Weighted sensitivity minimization for delay systems,” IEEE-TAC, vol. AC-31, no. 8, pp. 763–766, Aug. 1986.
J.S. Freudenberg and D.P. Looze, “A sensitivity tradeoff for plants with time delay,” IEEE-TAC, vol. AC-32, no. 2, pp. 99–104, Feb. 1987.
S. Fukata and M. Takata, “On sampling period sensitivities of the optimal stationary sampled-data linear regulator,” IJC, vol. 29, no. 1, pp. 145–158, 1979.
I. Gumowski, “Sensitivity of certain dynamic systems with respect to a small delay,” Automatica, vol. 10, pp. 659–674, 1974.
S. Hara and H.-K. Sung, “Sensitivity improvement by a stable controller in SISO digital control systems,” SCL, vol. 12, pp. 123–128, 1989.
K. Inoue, H. Akashi, K. Ogino, and Y. Sawaragi, “Sensitivity approaches to optimization of linear systems with time delay,” Automatica, vol. 7, pp. 671–679, 1971.
T. Ishihara, “Sensitivity properties of a class of discrete-time LQG controllers with computation delays,” SCL, vol. 11, pp. 299–307, 1988.
E.I. Jury and Y. Z. Tsypkin, “On the theory of discrete systems,” Automatica, vol. 7, pp. 89107, 1971.
M. Koda, “Sensitivity analysis of time-delay systems,” IJSS, vol. 12, no. 11, pp. 1389–1397, 1981.
A.J. Koivo, “Performance sensitivity of sampling systems–A unified approach,” JFI, vol. 287, no. 3, pp. 209–221, March 1969.
L.P. Kukhtenkov and A.I. Ruban, “The sensitivity of discontinuous systems described by differential-difference equations with lagging argument,” ECy, vol. 17, no. 6, pp. 136–141, 1979.
D.P. Lindorff, “Sensitivity in sampled-data systems,” IEEE-TAC, vol. AC-8, pp. 120–125, 1963.
A. Locatelli and S. Rinaldi, “Controllability versus sensitivity in linear discrete systems,” IEEE-TAC, vol AC-15, pp. 254–255, April 1970.
S.M. Melzer and B.C. Kuo, “Sampling period sensitivity of the optimal sampled data linear regulator,” Automatica, vol. 7, pp. 367–370, 1971.
C.P. Neuman and D.I. Schonbach, “Discrete weighted residual methods: A sensitive nonlinear boundary-value problem,” JOTA, vol. 22, no. 2, pp. 239–249, June 1977.
L. Pandolfi and A.W. Olbrot, “On the minimization of sensitivity to additive disturbances for linear-distributed parameter MIMO feedback systems,” IJC, vol. 43, no. 2, pp. 389–399, 1986.
EN. Rozenvasser, “General sensitivity equations of discontinuous systems,” ARC, no. 3, pp. 400–404, March 1967.
EN. Rozenvasser and R.M. Yusupov, “Sensitivity equations of pulse control systems,” ARC, no. 4, pp. 526–536, April 1969.
E.P. Ryan, “On the sensitivity of a time-optimal switching function,” IEEE-TAC, vol. AC-25, no. 2, pp. 275–277, April 1980.
M. Saeki, “Methods of solving a polynomial equation for an H°° optimal control problem for a single-input single-output discrete-time system,” IEEE-TAC, vol. AC-34, no. 2, pp. 166–168, Feb. 1989.
A.H. Shevelyev, “Analysis of sampled-data systems with variable parameters,” SAC, vol. 13, no. 3, pp. 14–22, 1968.
P. Stavroulakis, “Low sensitivity feedback law implementation for 2-D digital systems,” JFI, vol. 312, nos. 3 /4, pp. 217–229, Sept./Oct. 1981.
P. Stavroulakis and P.N. Paraskevopoulos, “Low-sensitivity observer-compensator design for two-dimensional digital systems,” Proc. IEE, vol. 129, Pt. D, no. 5, pp. 193–200, Sept. 1982.
P. Stavroulakis and S.G. Tzafestas, “State reconstruction in low-sensitivity design of 3dimensional systems,” Proc. lEE, vol. 130, Pt. D, no. 6, pp. 333–340, Nov. 1983.
K.L. Suryanarayanan and A.C. Soudack, “Method for the generation of sensitivity functions for nonlinear sampled-data systems,” Elect. Lett., vol. 6, no. 19, pp. 611–613, Sept. 1970.
K.E. Tait, “Sensitivity considerations and comparisons of sampling interval criteria for discrete-continuous feedback control systems,” IJC, vol. 6, no. 2, pp. 101–145, 1967.
V.I. Teverovskii, “On one particular case of a sampled-data system with variable parameters which change by jumps,” ARC, vol. 21, no. 1, pp. 42–46, Aug. 1960.
R. Tomovic and G.A. Bekey, “Adaptive sampling based on amplitude sensitivity,” IEEE-TAC, vol. AC-11, no. 2, pp. 282–284, April 1966.
R.K. Varshney and W.R. Perkins, “Sensitivity of linear time invariant sampled data systems to sampling period,” Automatica, vol. 10, pp. 317–319, 1974.
W.-Y. Yan and J.B. Moore, “On L2-sensitivity minimization of linear state-space systems,” IEEE-TCAS, Part I, vol. CAS-39, no. 8, pp. 641–648, 1992.
[O] Sensitivity Considerations in Distributed [Parameter] Systems
S. Abu El Ata-Doss, “Cost function sensitivity to small parameter variations for a class of distributed control systems,” JMAA, vol. 72, pp. 106–113, 1979.
S. Abu El Ata-Doss, “New technique of sensitivity reduction for distributed control systems,” AMO, vol. 5, pp. 217–229, 1979.
A. Bamberger, G. Chavent, and P. Lailly, “About the stability of the inverse problem in 1-D wave equations - Application to the interpretation of seismic profiles,” AMO, vol. 5, pp. 147, 1979.
C.-K. Chu and Y.-P. Shih, “Low sensitivity optimal control of a class of linear distributed systems,” IJC, vol. 16, no. 2, pp. 325–336, 1972.
J.M. Davis and W.R. Perkins, “Comparison sensitivity of distributed parameter systems,” IEEE-TAC, vol. AC-17, no. 1, pp. 100–105, Feb. 1972.
NF. Degtyareva, “Use of sensitivity functions for optimal control synthesis in systems with distributed parameters,” SA, vol. 19, no. 4, pp. 24–28, 1976.
C. Foias, A. Tannenbaum, and G. Zames, “Sensitivity minimization for arbitrary SISO distributed plants,” SCL, vol. 8, pp. 189–195, 1987.
M. Kelemen, Y. Kannai, and I. Horowitz, “Arbitrarily low sensitivity (ALS) in linear distributed systems using pointwise linear feedback,” IEEE-TAC, vol. AC-35, no. 9, pp. 10711075, Sept. 1990.
T. Kobayashi, “Controllability and stabilizability of sensitivity combined systems for distributed parameter systems,” IJC, vol. 35, no. 2, pp. 309–321, 1982.
V. Komkov, “Sensitivity techniques for systems with distributed parameters,” JMAA, vol. 128, pp. 443455, 1987.
M.C.Y. Kuo and M.N.B. Ayiku, “Synthesis of low-sensitivity optimal control in distributed parameter systems,” Proc. IEE, vol. 125, no. 6, pp. 550–554, June 1978.
I. Lasiecka and J. Sokolowski, “Sensitivity analysis of optimal control problems for wave equations,” SIAM-JCO, vol. 29, no. 5, pp. 1128–1149, 1991.
K. Malanowski and J. Sokolowski, “Sensitivity of solutions to convex, control constrained optimal control problems for distributed parameter systems,” JMAA, vol. 120, pp. 240–263, 1986.
A. Orbach and R. Fischl, “Performance index sensitivity of optimal control of first order in time-and space-distributed parameter systems,” IEEE-TAC, vol. AC-25, no. 2, pp. 314–317, April 1980.
K.C. Pedersen and L.R. Nardizzi, “Optimally sensitive control for distributed parameter systems,” IJC, vol. 16, no. 4, pp. 723–735, 1972.
H.J. Perlis, “Open-loop performance index sensitivity in a class of distributed optimal water management systems,” in Proc. Joint Auto. Contr., pp. 118–123, 1973.
S. Pohjolainen, “Robust controller for systems with exponentially stable strongly continuous semigroups,” JMAA, vol. 111, pp. 622–636, 1985.
W.A. Porter, “Sensitivity problems in distributive systems,” IJC, vol. 5, no. 5, pp. 393–412, 1967.
W.A. Porter, “Parameter sensitivity in distributive feedback systems,” IJC, vol. 5, no. 5, pp. 413–423, 1967.
A.I. Ruban, “Identification of distributed dynamic objects on the basis of a sensitivity algorithm,” ECy, vol. 9, no. 6, pp. 1137–1142, Nov./Dec. 1971.
J. Sokolowski, “Sensitivity analysis of control constrained optimal control problems for distributed parameter systems,” SIAM-JCO, vol. 25, no. 6, pp. 1542–1556, 1987.
J. Sokolowski, “Shape sensitivity analysis of boundary optimal control problems for parabolic systems,” SIAM-JCO, vol. 26, no. 4, pp. 763–787, 1988.
J. Sokolowski and J.P. Zolesio, “Shape design sensitivity analysis of plates and plane elastic solids under unilateral constraints,” JOTA, vol. 54, no. 2, pp. 361–382, 1987.
S.G. Tzafestas, “Eigenvalue and eigenfunction sensitivity of distributed-parameter systems (DPS),” IEEE-TAC, vol, AC-20, no. 1, pp. 172–174, 1975.
S.G. Tzafestas, “Sensitivity functions of distributed parameter eigenvalue control systems,” Elect. Leu., vol. 12, no. 1, pp. 4–6, Jan. 1976.
S.G. Tzafestas, “Eigenvalue control in distributed-parameter systems with parameter variations,” Proc. IEEE, vol. 64, no. 9, pp. 1444–1446, Sept. 1976.
S.G. Tzafestas and P.N. Paraskevopoulos, “Sensitive decoupling control of linear distributed-parameter systems,” IEEE-TAC, vol. AC-20, no. 1, pp. 151–153, Feb. 1975.
[P] Sensitivity Issues in Selected Multidisciplinary Optimization Methods, and Numerical Methods
D. Aze and M. Volle, “A stability result in quasi-convex programming,” JOTA, vol. 67, no. 1, pp. 175–184, 1990.
J.-F. M. Barthelemy and J. Sobieszczanski-Sobieski, “Optimum sensitivity derivatives of objective functions in nonlinear programming,” AIAA J., vol. 21, no. 6, pp. 913–915, June 1983.
R.G. Batson, “Extensions of Radstrom’s lemma with application to stability theory of mathematical programming,” JMAA, vol. 117, pp. 441–448, 1986.
C.S. Berger, “Numerical method for the design of insensitive control systems,” Proc. IEE, voL 120, no. 10, pp. 1283–1292, Oct. 1973.
C.S. Berger, “Numerical comparison of two methods of designing insensitive controllers,” Elect. Lett., vol. 11, no. 20, pp. 489–490, Oct. 1975.
M.J. Best and N. Chakravarti, “Stability of linearly constrained convex quadratic programs,” JOTA, vol. 64, no. 1, pp. 43–53, 1990.
J.H. Bigelow and N.Z. Shapiro, “Optimization problems with large parameters,” SIAM-JAM, vol. 24, no. 2, pp. 152, 163, March 1973.
R.N. Buie and J. Abraham, “Post-optimality sensitivity analysis in abstract spaces with applications to continuous-time programming problems,” JOTA, vol. 45, no. 3, pp. 347–373, 1985.
J.D. Buys and R. Gonin, “The use of augmented Lagrangian functions for sensitivity analysis in nonlinear programming,” MP, vol. 12, no. 2, p. 281–284, 1977.
R. Byers, “A Hamiltonian QR algorithm,” SIAM-JSSC, vol. 7, no. 1, pp. 212–229, 1986.
R. Byers, “A bisection method for measuring the distance of a stable matrix to the unstable matrices,” SIAM-JSSC, vol. 9, no. 5, pp. 875–881, 1988.
D. Chenais, “Optimal design of midsurface of shells: Differentiability proof and sensitivity computation,” AMO, vol. 16, pp. 93–133, 1987.
F.H. Clarke and P.D. Loewen, “The value function in optimal control: sensitivity, controllability, and time-optimality,” SIAM-JCO, vol. 24, no. 2, pp. 243–263, 1986.
W. Cook, A.M.H. Gerards, A. Schrijver, and E. Tardos, “Sensitivity theorems in integer linear programming,” MP, vol. 34, pp. 251–264, 1986.
S. Dafermos and A. Nagurney, “Sensitivity analysis for the asymmetric network equilibrium problem,” MP, vol. 28, pp. 174–184, 1984.
A. Dax, “The smallest point of a polytope,” JOTA, vol. 64, no. 2, pp. 429–432, 1990.
A. Deif, Sensitivity Analysis in Linear Systems. New York: Springer - Verlag, 1986.
R.S. Dembo, “Sensitivity analysis in geometric programming,” JOTA, vol. 37, no. 1, pp. 1–21, 1982.
J.W. Demmel, “A counterexample for two conjectures about stability,” IEEE-TAC voL AC-32, pp. 340–342, April 1987. [cf., [74].]
A.H. Evers, “Sensitivity analysis in dynamic optimization,” JOTA, vol. 32, no. 1, pp. 17–37, 1980.
S.D. Fassois, K.F. Eman, and S.M. Wu, “Sensitivity analysis of the discrete-to-continuous dynamic system transformation,” ASME-JDSMC, vol. 112, pp. 1–9, March 1990.
A.V. Fiacco, “Sensitivity analysis for nonlinear programming using penalty methods,” MP, vol. 10, no. 3, pp. 287–311, 1976. Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. New York: Academic Press, 1983. Reviewed by C.E. Lemke, SIAM R., vol. 27, no. 1, pp. 114115, 1985.
A.V. Fiacco, Ed., Sensitivity, Stability, and Parametric Analysis. ( A publication of the Mathematical Programming Society.) Amsterdam: North-Holland, 1984.
P.M. Gahinet, A.J. Laub, C.S. Kenney, and GA. Hewer, “Sensitivity of the stable discrete-time Lyapunov equation,” IEEE-TAC, vol. AC-35, no. 11, pp. 1209–1217, Nov. 1990.
F.W. Gembicki and Y.Y. Haimes, “Approach to performance and sensitivity multiobjective optimization: The goal attainment method,” IEEE-TAC, vol. AC-20, no. 6, pp. 769–771, 1975.
H. Gerencser, “Stability theorems for 2x2 hypermatrices,” JOTA, vol. 35, no. 1, pp. 1–7, 1981.
J.M. Goethals, “Le controle des erreurs dans les transmissions numeriques,” Automatisme, vol. XIX, no. 1, pp. 17–23, 1974.
P.H. Hammond and M.J. Duckenfield, “Automatic optimization by continuous perturbation of parameters,” Automatica, vol. 1, pp. 147–175, 1963.
G. Hewer and C. Kenney, “The sensitivity of the stable Lyapunov equation,” SIAM-JCO, vol. 26, no. 2, pp. 321–344, 1988.
W.J. Hopp, “Sensitivity analysis in discrete dynamic programming,” JOTA, vol. 56, no. 2, pp. 257–269, 1988.
R.H.F. Jackson and G.P. McCormick, “Second-order sensitivity analysis in factorable programming: Theory and applications,” MP, vol. 41, pp. 1–27, 1988.
R. Janin, “On sensitivity in an optimal control problem,” JMAA, vol. 60, no. 3, pp. 631–657, Oct. 1977.
V.M. Karas, “Stability of approximate solutions of the graph partitioning problem,” SJAIS, vol. 20, no. 3, pp. 55–59, 1987.
V.A. Kas’yanov and Y.P. Udartsev, “Increasing the stability of estimates by the least squares methods,” SJAIS, vol. 20, no. 3, pp. 44–48, 1987.
C. Kenney and G. Hewer, “The sensitivity of the algebraic and differential Riccati equations,” SIAM-JCO, vol. 28, no. 1, pp. 50–69, Jan. 1990.
S.W. Kim, P.G. Park, and W.H. Kwon, “Lower bounds for the trace of the solution of the discrete algebraic Riccati equation,” IEEE-TAC, vol. AC-38, no. 2, pp. 312–314, 1993.
V.G. Kolobov, “A method for increasing the stability of the numerical solution of differential equation systems,” SJAIS, vol. 22, no. 3, pp. 74–81, 1989.
N. Komaroff, “Upper bounds for the solution of the discrete Riccati equation,” IEEE-TAC, vol. AC-37, no. 9, pp. 1370–1373, 1992.
N. Komaroff and B. Shahian, “Lower summation bounds for the discrete Riccati and Lyapunov equations,” IEEE-TAC, vol. AC-37, no. 7, pp. 1078–1080, 1992.
M.M. Konstantinov and G.B. Pelova, “Sensitivity of the solutions to differential Riccati equations,” IEEE-TAC, vol. AC-36, no. 2, pp. 213–215, 1991.
V.S. Kouikoglou and Y.A. Phillis, “Trace bounds on the covariance of continuous-time systems with multiplicative noise,” IEEE-TAC, vol. AC-38, no. 1, pp. 138–142, 1993.
V.Y. Krivonozhko and A.I. Propoy, “The method of successive improvement of control in dynamic linear programming problems. I,” ECy, vol. 16, no. 3, pp. 1–12, 1978.
J. Kyparisis, “Sensitivity analysis in posynomial geometric programming,” JOTA, vol. 57, no. 1, pp. 85–121, 1988.
K. Malanowski, “Differential stability of solutions to convex, control constrained optimal control problems,” AMO, vol. 12, pp. 1–14, 1984.
K. Malanowski, “Stability and sensitivity of solutions to optimal control problems for systems with control appearing linearly,” AMO, vol. 16, pp. 73–91, 1987.
K. Malanowski, “Differential sensitivity of solutions of convex constrained optimal control prob- lems for discrete systems,” JOTA, vol. 53, no. 3, pp. 429–449, 1987.
K. Malanowski, “Sensitivity analysis of optimization problems in Hilbert space with application to optimal control,” AMO, vol. 21, pp. 1–20, 1990.
V.V. Mal’tsev, “Sufficient conditions for e-sensitivity in mathematical programming problems,” SAC, vol. 12, no. 5, pp. 35–39, 1979.
J.M. Martin and G.A. Hewer, “Smallest destablizing perturbations for linear systems,” ITC, vol. 45, no. 5, pp. 1495–1504, 1987. Comments by C.B. Soh, ibid., vol. 49, no. 5, pp. 18131814, 1989.
T. Masuda, “Hierarchical sensitivity analysis of priority used in analytic hierarchy process,” IJSS, vol. 21, no. 2, pp. 415–427, 1990.
V.S. Mel’nik, “Nonconvex optimization problems for quasilinear distributed-parameter systems,” SJAIS, vol. 21, no. 2, pp. 80–83, 1988.
M. Mrabti and A. Hmamed, “Bounds for the solution of the Lyapunov matrix equation–A unified approach,” SCL, vol. 18, pp. 73–81, 1992.
P.H. Naccache, “Stability in multicriteria optimization,” JMAA, vol. 68, pp. 441–453, 1979.
A. Neumaier, “Rigorous sensitivity analysis for parameter-dependent systems of equations,” JMAA, vol. 144, pp. 16–25, 1989.
K.C. Park and J.C. Chiou, “Stabilization of computational procedures for constrained dynamical systems,” JGCD, vol. 11, no. 4, pp. 365–370, 1988.
D.W. Peterson, “On sensitivity in optimal control problems,” JOTA, vol. 13, no. 1, pp. 56–73, 1974.
B.D. Prudovskiy, “Stability of solutions in certain nonlinear optimization problems,” ECy, vol. 17, no. 1, pp. 151–153, 1979.
V. Rupnik, “Stability conditions on continuous dynamic linear programming,” JMAA, vol. 119, pp. 171–181, 1986.
J.K. Sengupta, “Sensitivity analysis for a linearized method of geometric programming,” IJSS, vol. 8, no. 2, pp. 153–161, 1977.
A. Shapiro, “Second order sensitivity analysis and asymptotic theory of parameterized nonlinear programs,” MP, vol. 33, pp. 280–299, 1985.
A. Shapiro, “Sensitivity analysis of nonlinear programs and differentiability properties of metric projections,” SIAM-JCO, vol. 26, pp. 628–645, 1988.
A. Shapiro, “Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton,” AMO, vol. 18, pp. 215–229, 1988.
A. Shapiro, “On concepts of directional differentiability,” JOTA, vol. 66, no. 3, pp. 477–487, 1990.
S. Shiraishi, “First-order and second-order c-directional derivatives of a marginal function in convex programming with linear inequality constraints,” JOTA, vol. 66, no. 3, pp. 489–502, 1990.
J. Sokolowski, “Sensitivity analysis of contact problems with prescribed friction,” AMO, vol. 18, pp. 99–117, 1988.
A.M. Steinberg, “Application of relaxed solutions to minimum sensitivity optimal control,” JOTA, vol. 10, no. 4, pp. 178–186, 1972.
T. Tanino, “Stability and sensitivity analysis in convex vector optimization,” SIAM-JCO, vol. 26, no. 3, pp. 521–536, 1988.
T. Tanino, “Sensitivity analysis in multiobjective optimization,” JOTA, vol. 56, no. 3, pp. 479–499, 1988.
R.L. Tobin, “Sensitivity analysis for variational inequalities,” JOTA, vol. 48, no. 1, pp. 191204, 1986.
M.D. Troutt, “A stability concept for matrix game optimal strategies and its application to linear programming sensitivity analysis,” MP, vol. 36, pp. 353–361, 1986.
K.C.Q. Tsai, D.M. Auslander, “A statistical methodology of designing controllers for minimum sensitivity of parameter variations,” ASME-JDSMC, voL 110, pp. 126–133, June 1988.
C. Van Loan, “How near is a stable matrix to an unstable matrix,” in Linear Algebra and Its Role in Systems Theory, in Proc. AMS-IMS-SIAM Conf. held July 29 to Aug. 4, 1984 (R.A. Brualdi, et al. Eds.), Contemporary Mathematics, American Mathematical Society vol. 47, pp. 465–478, 1985. [cf., [20].]
J. Varah, “On the separation of two matrices,” SIAM-JNA, vol. 16, pp. 216–222, 1979.
R.B. Vinter, “Optimality and sensitivity of discrete time processes,” CCy, vol. 17, nos. 2/3, pp. 191–211, 1988.
W. Von Dinkelbach, Sensitivitatsanalysen und parametrische Programmierung. Berlin: Springer–Verlag, 1969. Reviewed by S.I. Gass, SIAM R., vol. 12, no. 1, pp. 165–166, 1970.
A.N. Voronin, “A multicriteria variational problem for deterministic and statistically specified actions,” SJAIS, vol. 21, no. 5, pp. 37–42, 1988.
A.N. Voronin and V.V. Pavlov, “Solution of multicriterial variational problems under indeterminacy conditions,” SJAIS, vol. 21, no. 2, pp. 23–31, 1988.
K. Watanabe and H. Shimizu, “Parameter optimizing software system using Pade’s computation method of transient response,” EEJ, vol. 95, no. 2, pp. 119–125, March/April 1975.
P. Whittle, “Entropy-minimising and risk-sensitive control rules,” SCL, vol. 13, pp. 1–7, 1989.
P. Whittle, “A risk-sensitive maximum principle,” SCL, vol. 15, pp. 183–192, 1990.
P. Whittle, “A risk-sensitive maximum principle: The case of imperfect state observation,” IEEE-TAC, vol. AC-36, no. 7, pp. 793–801, 1991.
P. Whittle and J. Kuhn, “A Hamiltonian formulation of risk-sensitive linear/quadratic/Gaussian control,” IJC, vol. 43, no. 1, pp. 1–12, 1986.
L.A. Wolsey, “Integer programming duality: Price functions and sensitivity analysis,” MP, vol. 20, pp. 173–195, 1981.
J.-H. Xu and R.E. Skelton, “An improved covariance assignment theory for discrete systems,” IEEE-TAC, vol. AC-37, no. 10, pp. 1588–1591, 1992.
J. Zowe and S. Kurcyusz, “Regularity and stability for the mathematical programming problem in Banach spaces,” AMO, vol. 5, pp. 49–62, 1979.
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Eslami, M. (1994). Sensitivity Reduction and Robustness. In: Theory of Sensitivity in Dynamic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01632-9_6
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