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Robust H ∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals

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Abstract

This paper deals with the problems of robust stabilization and robust H ∞ control for time-delay stochastic systems with Markovian jump parameters and convex polytopic uncertainties. The purpose is the design of state feedback controllers such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H ∞ performance level. Sufficient conditions for the solvability of the problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that desired state feedback controllers can be designed by solving a set of linear matrix inequalities.

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References

  1. E. K. Boukas and P. Shi. Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters. Int. J. Robust & Nonlinear Control, 8:1155–1167, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. E. K. Boukas, Z. K. Liu, and G. X. Liu. Delay-dependent robust stability and H ∞ control of jump linear systems with time-delay. Int. J. Control, 74:329–340, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Chen, J. Lam, and S. Xu. Memory state feedback guaranteed cost control for neutral delay systems. Int. J. Innovative Computing, Information and Control, 2:293–303, 2006.

    Article  Google Scholar 

  4. C. E. de Souza and M. D. Fragoso. H ∞ control for linear systems with Markovian jumping parameters. Control Theory and Advance Technology, 9:457–466, 1993.

    Google Scholar 

  5. Y. Ji and H. J. Chizeck. Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control, 35:777–788, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  6. X. Mao. Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl., 79:45–67, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  7. X. Mao. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Automat. Control, 47:1604–1612, 2002.

    Article  MathSciNet  Google Scholar 

  8. P. Shi and E. K. Boukas. H ∞-control for Markovian jumping linear systems with parametric uncertainty. J. Optim. Theory Appl., 95:75–99, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  9. S. H. Song and J. K. Kim. H ∞ control of discrete-time linear systems with norm-bounded uncertainties and time delay in state. Automatica, 34:137–139, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Xu and T. Chen. Robust H ∞ control for uncertain stochastic systems with state delay. IEEE Trans. Automat. Control, 47:2089–2094, 2002.

    Article  MathSciNet  Google Scholar 

  11. S. Xu and C. Yang. H ∞ state feedback control for discrete singular systems. IEEE Trans. Automat. Control, 45:1405–1409, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Xu, P. Van Dooren, R. Stefan, and J. Lam. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Automat. Control, 47:1122–1128, 2002.

    Article  MathSciNet  Google Scholar 

  13. S. Xu, T. Chen, and J. Lam. Robust H ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Automat. Control, 48:900–907, 2003.

    Article  MathSciNet  Google Scholar 

  14. S. Xu, J. Lam, X. Mao, and Y. Zou. A new LMI condition for delay-dependent robust stability of stochastic time-delay systems. Asian Journal of Control, 7:419–423, 2005.

    Article  MathSciNet  Google Scholar 

  15. S. Xu, J. Lam, and Y. Zou. New results on delay-dependent robust H ∞ control for systems with time-varying delays. Automatica, 42:343–348, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  16. S. Xu, P. Shi, Y. Chu, and Y. Zou. Robust stochastic stabilization and H ∞ control of uncertain neutral stochastic time-delay systems. J. Math. Anal. Appl., 314:1–16, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  17. X. Xue and D. Qiu. Robust H ∞-compensator design for time-delay systems with norm-bounded time-varying uncertainties. IEEE Trans. Automat. Control, 45:1363–1369, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  18. B. Zhang, S. Zhou, and S. Xu. Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays. International Journal of Systems Science, 38:611–621, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. Zhou, G. Feng, L. James, and S. Xu. Robust H ∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions. Information Sciences, 174:197–217, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  20. X. Zhu, Y. Soh, and L. Xie. Robust Kalman filter design for discrete time-delay systems. Circuit, Syst., Sig. Process., 21:319–335, 2002.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Jianwei Xia

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Jianwei Xia & Bo Song

  3. College of Electrical and Electronic Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing, 210042, People’s Republic of China

    Junwei Lu

Authors
  1. Jianwei Xia
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  2. Bo Song
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  3. Junwei Lu
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Correspondence to Bo Song.

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Xia, J., Song, B. & Lu, J. Robust H ∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals. Circuits Syst Signal Process 27, 331–349 (2008). https://doi.org/10.1007/s00034-008-9017-z

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  • DOI: https://doi.org/10.1007/s00034-008-9017-z

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