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Science China Information Sciences

, Volume 54, Issue 12, pp 2615–2630 | Cite as

H 2/H control of networked control system with random time delays

  • Li Qiu
  • BuGong Xu
  • ShanBin LiEmail author
Research Papers

Abstract

This paper investigates the H 2/H control problem for a class of discrete-time networked control systems with random communication time delays. Both sensor-to-controller (S-C) and controller-to-actuator (C-A) random network-induced delays are considered. Two independent Markov chains are used to model the S-C and C-A random delays. The resulting closed-loop system is a jump linear time-delay system induced by two Markov chains. Sufficient conditions for existence of H 2/H controller are established by free-weighting matrix and stochastic Lyapunov functions. A simulation example illustrates the effectiveness of the proposed method.

Keywords

h2/h control networked control systems markov chains random time delays 

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References

  1. 1.
    Zhang W, Branicky M S, Phillips S M. Stability of networked control systems. IEEE Control Syst Mag, 2001, 21: 84–99CrossRefGoogle Scholar
  2. 2.
    Walsh G C, Ye H, Bushnell L G. Stability analysis of networked control systems. IEEE Trans Control Syst Tech, 2002, 10: 438–446CrossRefGoogle Scholar
  3. 3.
    Yang T C. Networked control systems: A brief survey. Proc IEE Control Theory Appl, 2006, 153: 403–412CrossRefGoogle Scholar
  4. 4.
    Ji K, Kim W J. Robust control for networked control systems with admissible parameter uncertainties. Int J Control Autom Syst, 2007, 5: 372–378Google Scholar
  5. 5.
    Jia T G, Niu Y G, Wang X Y. H control for networked systems with data packet dropout. Int J Control Autom Syst, 2010, 8: 198–203CrossRefGoogle Scholar
  6. 6.
    Zhang L Q, Shi Y, Chen T, et al. A new method for stabilization of networked control systems with random delays. IEEE Trans Autom Control, 2005, 50: 1177–1181CrossRefMathSciNetGoogle Scholar
  7. 7.
    Shi Y, Yu B. Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans Autom Control, 2009, 54: 1668–1674CrossRefMathSciNetGoogle Scholar
  8. 8.
    Che W W, Wang J L, Yang G H. Observer-based H control in multiple channel networked control systems with random packet dropouts. J Control Theory Appl, 2010, 8: 359–367CrossRefGoogle Scholar
  9. 9.
    Zhang W A, Yu L. Modeling and control of networked control systems with both network-induced delay and packetdropout. Automatica, 2008, 44: 3206–3210CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Cloosterman M B G, Wouw N van de, Heemels W P M H, et al. Stability of networked control systems with uncertain time-varying delays. IEEE Trans Autom Control, 2009, 54: 1575–1579CrossRefGoogle Scholar
  11. 11.
    Hu S S, Zhu Q X. Stochastic optimal control and analysis of networked control systems with long delay. Automatica, 2003, 39: 1877–1884CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Zou Y Y, Li S Y. Receding horizon estimation to networked control systems with multirate scheme. Sci China Ser F-Inf Sci, 2009, 52: 1103–1112CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Wang X H, Yang Z Q, Qian Q, et al. Analysis and control of networked control systems with time-delay and stochastic packet-dropout process. In: Chinese Control and Decision Conference, Shanghai, 2010. 1936–1941Google Scholar
  14. 14.
    Xie D X, Han X D, Huang H, et al. Research on robust mean square stability of networked control systems with packet dropout. J Syst Eng Electr, 2010, 21: 95–101Google Scholar
  15. 15.
    Shi Y, Yu B, Huang J. Mixed H 2/H control of networked control systems with random delay modeled by Markov chains. In: 2009 American Control Conference, St. Louis, Mo, 2009. 4038–4043Google Scholar
  16. 16.
    Zhang W H, Huang Y L, Xie L H. Infinite horizon stochastic H 2/H control for discrete-time systems with state and disturbance dependent noise. Automatica, 2008, 44: 2306–2316CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Chen B S, Zhang W. Stochastic H 2/H control with state-dependent noise. IEEE Trans Autom Control, 2004, 49: 45–57CrossRefGoogle Scholar
  18. 18.
    Muradore R, Picci G. Mixed H 2/H control: The discrete-time case. Syst Control Lett, 54: 1–13Google Scholar
  19. 19.
    Costa O L V, Marques R P. Mixed H 2/H control of discrete-time Markovian jump linear systems. IEEE Trans Autom Control, 1998, 43: 95–100CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Khargonekar P P, Rotea M A. Mixed H 2/H control: A convex optimization approach. IEEE Trans Autom Control, 1991, 36: 824–837CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Du C L, Xie L H, Teoh J N, et al. An improved mixed H 2/H control design for hard disk drives. IEEE Trans Autom Control, 2005, 13: 832–839Google Scholar
  22. 22.
    Li S B, Sun Y X. Networked guaranteed cost control for uncertain discrete-time Markovian jump linear systems. Dynam Contin, Discrete Impuls Syst Ser B: Appl Algor, 2008, 15: 129–146zbMATHGoogle Scholar
  23. 23.
    Zhang L X, Boukas E K, Lam J. Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans Autom Control, 2008, 53: 2458–2464CrossRefMathSciNetGoogle Scholar
  24. 24.
    Wang Y F, Wang C H, Huang X. Guaranteed cost control with random communication delays via jump linear system approach. In: The 8th International Conference on Control, Automation, Robotics and Vision, Kunming, China, 2004. 298–303Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.College of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.College of Mechatronics and Control EngineeringShenzhen UniversityShenzhenChina

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