Skip to main content
SpringerLink
Log in

Deterministic and stochastic linear periodic systems

  • Conference paper
  • First Online:
Time Series and Linear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 86))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bailey, J.E. (1973): Periodic Operation of Chemical Reactors: A Review. Chem. Eng. Commun. 1, 111–124.

    Google Scholar 

  • Bekir, E. and R.S. Bucy (1976): Periodic Equilibria for Matrix Riccati Equations. Stochastics 2, 1–104.

    Google Scholar 

  • Belevitch, V. (1968): Classical Network Theory. Holden Day, San Francisco.

    Google Scholar 

  • Bernstein, D.S and E.G. Gilbert (1980): Optimal Periodic Control: The п Test Revisited. IEEE Trans. Automatic Control AC-25, 673–684.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1984,a): Can the Kalman Canonical Decomposition be performed for a Discrete-time Linear Periodic System? 1st Latin American Conference on Automatica, Campina Grande, Brazil, 449–453.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1984,b): Canonical Decomposition and Discrete-time Linear Systems. 23rd Conference of Decision and Control, Las Vegas, U.S.A., 1737, 1738.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1984,c): Four Equivalent Notions of Stabilizability of Periodic Linear Systems. 3rd American Control Conference, San Diego, U.S.A., 1321–1323.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1985,a): Reachability and Controllability of Discrete-time Linear Systems. IEEE Trans. Automatic Control 30, 399–491.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1985,b): Discrete-time Linear Periodic Systems: Grammian and Modal Criteria for Reachability and Controllability. International J. Control 41, 899–928.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1985,c): Stabilizability and Detectability of Linear Periodic Systems. Systems and Control Letters 6, 141–145. Plus Addendum, to appear in Systems and Control Letters (1986), 7, 73.

    Google Scholar 

  • Bittanti, S. and P. Bolzern (1986): On the Structure Theory of Discrete-time Linear Systems. International J. Systems Science, 17, 33–47.

    Google Scholar 

  • Bittanti, S., P. Bolzern and P. Colaneri (1984): Stability Analysis of Linear Periodic Systems via the Lyapunov Equation. 9th IFAC World Congress, Budapest, 8, 169–172.

    Google Scholar 

  • Bittanti, S., P. Bolzern and P. Colaneri (1985): The Extended Periodic Lyapunov Lemma. Automatica 5, 603–605.

    Google Scholar 

  • Bittanti, S., P. Bolzern, P. Colaneri and G. Guardabassi (1983): H and K-Controllability of Linear Periodic Systems. 22nd Conference on Decision and Control, S. Antonio, U.S.A., 1376–1379.

    Google Scholar 

  • Bittanti, S. and P. Colaneri (1986): Lyapunov and Riccati Equations: Periodic Inertia Theorems. IEEE Trans. Automatic Control (to appear).

    Google Scholar 

  • Bittanti, S., P. Colaneri and G. De Nicolao (1986): Discrete-time Periodic Systems: a note on the Reachability and Controllability interval length. Centro Teoria Sistemi, Politecnico di Milano, Int. Rep. 86-003.

    Google Scholar 

  • Bittanti, S., P. Colaneri and G. Guardabassi (1984): H-Controllability and Observability of Linear Periodic Systems. SIAM J. Control and Optimization 22, 889–893.

    Google Scholar 

  • Bittanti, S., G. Fronza and G. Guardabassi (1973): Periodic Control: A Frequency Domain Approach. IEEE Trans. Automatic Control 18, 33–38.

    Google Scholar 

  • Bittanti, S., G. Guardabassi, C. Maffezzoni and L. Silverman (1978): Periodic Systems: Controllability and the Matrix Riccati Equation. SIAM J. Control and Optimization 16, 37–40.

    Google Scholar 

  • Bittanti, S. and D.B. Hernandez (1986): The Simple Pendulum as an Illustrative Example of the Periodic Control Problem. Centro Teoria dei Sistemi, Politecnico di Milano, Int. Rep. 86-010.

    Google Scholar 

  • Bolzern, P. (1986): Criteria for Reachability, Controllability and Stabilizability of Discrete-time Linear Periodic Systems. V Polish-English Seminar on Real-Time Process Control, Warsaw, Poland.

    Google Scholar 

  • Bolzern, P. and P. Colaneri (1986): Existence and Uniqueness Conditions for the Periodic Solutions of the Discrete-time Periodic Lyapunov Equation. Centro Teoria dei Sistemi, Politecnico di Milano, Int. Rep. 86-011.

    Google Scholar 

  • Brockett, R.W. (1970): Finite Dimensional Linear Systems. J. Wiley and Sons.

    Google Scholar 

  • Brunovsky, P. (1969): Controllability and Linear Closed loop Controls in Linear Periodic Systems. J. Differential Equations 6, 296–313.

    Google Scholar 

  • Chen, C.T. (1970): Introduction to Linear System Theory. Holt, Rinehart and Winston.

    Google Scholar 

  • Colonius, F. (1985,a): Optimality for Periodic Control of Functional Differential Systems. J. Mathematical Analysis and Applications (to appear).

    Google Scholar 

  • Colonius, F. (1985,b): The High Frequency Pi-Criterion for Retarded Systems. IEEE Trans. Automatic Control 11, 1045–1048.

    Google Scholar 

  • DaPrato, G. (1984): Periodic Solutions of Infinite Dimensional Riccati Equations. Rendiconti Accademia Nazionale dei Lincei, (to appear).

    Google Scholar 

  • Dorato, P. and A.H. Levis (1971): Optimal Linear Regulators: the Discrete-time Case. IEEE Trans. Automatic Control 6, 613–620.

    Google Scholar 

  • Dorato, P. and H.K. Knudsen (1979): Periodic Optimization with Applications to Solar Energy Control. Automatica 15, 673–679.

    Google Scholar 

  • Gardner, W.A. and D.E. Franks (1975): Characterization of Cyclo-stationary Random Processes. IEEE Trans. Information Theory 21, 1–24.

    Google Scholar 

  • Gilbert, E.G. (1977): Optimal Periodic Control: A General Theory of Necessary Conditions. SIAM J. Control and Optimization 15, 717–746.

    Google Scholar 

  • Gilbert, E.G. and D.T. Lyons (1981): The Improvement of Aircraft Specific Range by Periodic Control. AIAA Guidance and Control Conference, Albuquerque.

    Google Scholar 

  • Graham, A. (1981): Kronecker Products and Matric Calculus with Applications. Ellis Horwood Limited, Chichester.

    Google Scholar 

  • Grasselli, O.M. (1984): A Canonical Decomposition of Linear Periodic Discrete-time Systems. International J. Control 40, 201–214.

    Google Scholar 

  • Guardabassi, G. (1971): Optimal Steady State Versus Periodic Control. Ricerche di Automatica 2, 240–252.

    Google Scholar 

  • Guardabassi, G. (1976): The Optimal Periodic Control Problem. Journal A 17, 75–83.

    Google Scholar 

  • Halanay, A. (1966): Differential Equations. Academic Press, New York.

    Google Scholar 

  • Hautus, M.L.J. (1969): Controllability and Observability Conditions of Linear Autonomous Systems. Indag. Math. 72 443–448.

    Google Scholar 

  • Hernandez, V. and L. Jodar (1985): Boundary Problems and Periodic Riccati Equations. IEEE Trans. Automatic Control 11, 1131–1133.

    Google Scholar 

  • Hewer, G.A. (1975): Periodicity, Detectability and the Matrix Riccati Equation. SIAM J. Control 13, 1235–1251.

    Google Scholar 

  • Horn, F.J.M. and R.C. Lin (1967): Periodic Processes: A Variational Approach. Ind. Eng. Chem. Process Des. Dev. 6, I, 21–30.

    Google Scholar 

  • Horn, F.J.M. and J.E. Bailey (1968): An Application of the Theorem of Relaxed Control to the Problem of Increasing Catalyst Selectivity. J. Optimization Theory and Applications 2, 441–449.

    Google Scholar 

  • Houlihan, S.C., E.M. Cliff and H.J. Kelley (1982): Study of Chattering Cruise, Journal Aircraft 19, 119–124.

    Google Scholar 

  • Johnson, C.D. (1966): Invariant Hyperplanes for Linear Dynamical Systems. IEEE Trans. Automatic Control 11, 113–116.

    Google Scholar 

  • Kabamba, P.T. (1985): Monodromy Eigenvalue Assignment in Linear Periodic Systems. 24th Conference on Decision and Control, Ft. Lauderdale, U.S.A., 177, 178.

    Google Scholar 

  • Kalman, R.E. (1969): Theory of Regulators for Linear Plants. In: Kalman R.E., P.L. Falb and M.A. Arbib: Topics in Mathematical System Theory. McGraw-Hill Co., New York.

    Google Scholar 

  • Kano, H. and T. Nishimura (1979): Periodic Solutions of Matrix Riccati Equations with Detectability and Stabilizability. International J. Control 29, 471–487.

    Google Scholar 

  • Kern, G. (1980): Linear Closed-loop Control in Linear Periodic Systems with Application to Spin-stabilized Bodies. International J. Control 31, 905–916.

    Google Scholar 

  • Khandelwal, D.N., J. Sharma and L.M. Ray (1979): Optimal Periodic Maintenance of a Machine. IEEE Trans. Automatic Control 24, 513.

    Google Scholar 

  • Khargonekar, P.P., K. Poolla and A. Tannenbaum (1985): Robust Control of Linear Time-invariant Plants Using Periodic Compensation. IEEE Trans. Automatic Control 11, 1088–1098.

    Google Scholar 

  • Kono, M. (1980): Eigenvalue Assignment in Linear Periodic Discrete-time Systems. International J. Control 1, 149–158.

    Google Scholar 

  • Maffezzoni, C. (1974): Hamilton-Jacobi Theory for Periodic Control Problems. J. Optimization Theory and Applications 14, 21–29.

    Google Scholar 

  • Markus, L. (1973): Optimal Control of Limit Cycles or what Control Theory can do to Cure a Heart Attack or to Cause One. Symposium on Ordinary Differential Equations, Minneapolis, Minnesota (1972). W.A. Harris, Y. Sibuya, eds., Springer-Verlag, Berlin.

    Google Scholar 

  • Matsubara, M., N. Nishimura, N. Watanabe and K. Onogi (1981): Periodic Control Theory and Applications. Research Reports of Automatic Control Laboratory Vol. 28, Faculty of Engineering, Nagoya University.

    Google Scholar 

  • Matsubara, M. and K. Onogi (1978): Stabilized Suboptimal Periodic Control of a Chemical Reactor. IEEE Trans. Automatic Control 23, 1005–1008.

    Google Scholar 

  • Meyer, R.A. and C.S. Burrus (1976): Design and Implementation of Multirate Digital Filters. IEEE Trans. Acoustics, Speech and Signal Processing 1, 53–58.

    Google Scholar 

  • Nistri, P. (1983): Periodic Control Problems for a Class of Nonlinear Periodic Differential Systems. Nonlinear Analysis, Theory, Methods and Applications 7, 79–90.

    Google Scholar 

  • Noldus, E. (1975): A Survey of Optimal Periodic Control of Continuous Systems. Journal A 16, 11–16.

    Google Scholar 

  • Onogi, K. and M. Matsubara (1980): Structure Analysis of Periodically Controlled Chemical Processes. Chem. Eng. Sci. 34, 1009–1019.

    Google Scholar 

  • Popov, V.M. (1973): Hyperstability of Control Systems. Springer, Berlin.

    Google Scholar 

  • Schädlich, K., U. Hoffmann and H. Hofmann (1983): Periodical Operation of Chemical Processes and Evaluation of Conversion Improvements. Chemical Engineering Science 38, 1375–1384.

    Google Scholar 

  • Shayman, M.A. (1984): Inertia Theorems for the Periodic Lyapunov Equation and Periodic Riccati Equation. Systems and Control Letters 4, 27–32.

    Google Scholar 

  • Shayman, M.A. (1985): On the Phase Portrait of the Matrix Riccati Equation Arising from the Periodic Control Problem. SIAM. J. Control and Optimization 23, 717–751.

    Google Scholar 

  • Sincic, D. and J.E. Bailey (1978): Optimal Periodic Control of Variable Time-delay Systems. International J. Control 27, 547–555.

    Google Scholar 

  • Speyer, J.L. (1973): On the Fuel Optimality of Cruise, J. Aircraft 10, 763–764.

    Google Scholar 

  • Speyer, J.L. (1976): Non-optimality of Steady-state Cruise for Aircraft. AIAA Journal 14, 1604–1610.

    Google Scholar 

  • Speyer, J.L. and R.T. Evans (1984): A Second Variational Theory of Optimal Periodic Processes. IEEE Trans. Automatic Control 29, 138–148.

    Google Scholar 

  • Valko, P. and G.A. Almasy (1982): Periodic Optimization of Hammerstein-type Systems. Automatica 18, 245–148.

    Google Scholar 

  • Watanabe, N., Y. Nishimura and M. Matsubara (1976): Singular Control Test for Optimal Periodic Control Problems. IEEE Trans. Automatic Control 21, 609–610.

    Google Scholar 

  • Watanabe, N., K. Onogi and M. Matsubara (1981): Periodic Control of Continuous Stirred Tank Reactors — I, Chem. Eng. Sci. 36, 809–818, II ibid. 37, 745–752.

    Google Scholar 

  • Watanabe, N., H. Kurimoto and M. Matsubara (1984): Periodic Control of Continuous Stirred Tank Reactors — III, Case of multistage reactors. Chem. Eng. Sci. 39, 31–36.

    Google Scholar 

  • Wimmer, H.K. and A.D. Ziebur (1975): Remarks on Inertia Theorems for Matrices. Czechoslovak Mathematical Journal 25, 556–561.

    Google Scholar 

  • Wong, E. and B. Hajek (1985): Stochastic Processes in Engineering. Springer-Verlag, Berlin.

    Google Scholar 

  • Wonham, W.M. (1968): On a Matrix Riccati Equation for Stochastic Control. SIAM Journal Control 6, 681–698.

    Google Scholar 

  • Yakubovich, V.A. and V.M. Starzhinskii (1975): Linear Differential Equations with Periodic Coefficients. J. Wiley, New York.

    Google Scholar 

Download references

Authors
  1. Sergio Bittanti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Sergio Bittanti

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Bittanti, S. (1986). Deterministic and stochastic linear periodic systems. In: Bittanti, S. (eds) Time Series and Linear Systems. Lecture Notes in Control and Information Sciences, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043803

Download citation

  • DOI: https://doi.org/10.1007/BFb0043803

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16903-1

  • Online ISBN: 978-3-540-47155-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation