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Complete damping of a linear autonomous differential-difference system by a controller of the same type

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Abstract

For a spectrally controllable linear autonomous system of retarded type with commensurable delays, we construct a dynamic state feedback ensuring a complete damping of the original system. The closed-loop system is of retarded type as well. The results are illustrated by an example.

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References

  1. Manitius, A.Z. and Olbrot, A.W., Finite Spectrum Assignment Problem for Systems with Delays, IEEE Trans. Automat. Control, 1979, no. 4, pp. 541–553.

  2. Krasovskii, N.N. and Osipov, Yu.S., On the Stabilization of the Motion of a Controlled Object with a Delay in the Control System, Izv. Akad. Nauk SSSR Tekhn. Kibern., 1963, vol. 6, pp. 3–15.

    Google Scholar 

  3. Osipov, Yu.S., On Stabilization of Control Systems with Delay, Differ. Uravn., 1965, vol. 1, no. 5, pp. 605–618.

    MathSciNet  MATH  Google Scholar 

  4. Bhat, K.P. and Koivo, H.N., Model Characterization of Controllability and Observability of Time-Delay Systems, IEEE Trans. Automat. Control, 1976, no. 2, pp. 292–293.

  5. Marchenko, V.M., On the Controllability of Linear Systems with Delay, Dokl. Akad. Nauk SSSR, 1977, vol. 236, no. 5, pp. 1083–1086.

    MathSciNet  Google Scholar 

  6. Watanabe, K., Ito, M., and Kaneko, M., Finite Spectrum Assignment Problem for Systems with Multiple Commensurate Delays in State Variables, Internat. J. Control, 1983, vol. 38, no. 5, pp. 913–926.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bulatov, V.I., Spectral Controllability of Systems with Lag, Differ. Uravn., 1977, vol. 13, no. 10, pp. 1876–1878.

    MathSciNet  MATH  Google Scholar 

  8. Asmykovich, I.K. and Marchenko, V.M., Spectrum Control in Systems with Delay, Avtomat. i Telemekh., 1976, no. 7, pp. 5–14.

  9. Bulatov, V.I., Spectral Reducibility of Systems with Lag, Vestn. Beloruss. Gos. Univ. Ser. I, 1979, no. 3, pp. 78–80.

  10. Metel’skii, A.V., Spectral Reducibility of Differential Systems with Delay with the Use of a Dynamic Controller, Differ. Uravn., 2011, vol. 47, no. 11, pp. 1621–1637.

    MathSciNet  Google Scholar 

  11. Metel’skii, A.V. and Karpuk, V.V., On the Properties of Pointwise Degenerate Linear Autonomous Control Systems. I, Avtomat. i Telemekh., 2009, no. 10, pp. 22–34.

  12. Karpuk, V.V. and Metel’skii, A.V., Complete Damping and Stabilization of Linear Autonomous Systems with Delay, Izv. Ross. Akad. Nauk Teor. Sist. Upravl., 2009, no. 6, pp. 19–28.

  13. Kappel, F., On Degeneracy of Functional-Differential Equations, J. Differential Equations, 1976, vol. 22, no. 2, pp. 250–267.

    Article  MathSciNet  MATH  Google Scholar 

  14. Kalman, R., Falb, P., and Arbib, M., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971.

    MATH  Google Scholar 

  15. Kappel, F., Degenerate Difference-Differential Equations. Algebraic Theory, J. Differential Equations, 1977, vol. 24, no. 1, pp. 99–126.

    Article  MathSciNet  MATH  Google Scholar 

  16. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988.

    MATH  Google Scholar 

  17. Karpuk, V.V. and Metel’skii, A.V., Critical Case in the Construction of a Complete Damping Controller for a Linear Autonomous Delay System, in Mezhdunar. mat. konf. “Pyatye Bogdanovskie chteniya po obyknovennym differentsial’nym uravneniyam:” Tez. dokl. (Abstr. Int. Math. Conf. “Fifth Bogdanov Readings on Ordinary Differential Equations”), Minsk, 2010, pp. 88–89.

  18. Popov, V.M., Giperustoichivost’ avtomaticheskikh sistem (Hyperstability of Automated Systems), Moscow, 1970.

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Authors and Affiliations

  1. Belarus National Technical University, Minsk, Belarus

    A. V. Metel’skii

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  1. A. V. Metel’skii
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Original Russian Text © A.V. Metel’skii, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 9, pp. 1240–1255.

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Metel’skii, A.V. Complete damping of a linear autonomous differential-difference system by a controller of the same type. Diff Equat 48, 1219–1235 (2012). https://doi.org/10.1134/S0012266112090030

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