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Stability of linear discrete switched systems with delays based on average dwell time method

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Abstract

This paper deals with the problem of exponential stability for a class of linear discrete switched systems with constant delays. The switched systems consist of stable and unstable subsystems. Based on the average dwell time method, some switching signals will be found to guarantee exponential stability of these systems. The explicit state decay estimation is also given in the form of the solutions of linear matrix inequalities (LMIs). An example relating to networked control systems (NCSs) illustrates the effectiveness of the proposed method.

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References

  1. Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Contr, 1998, 43: 475–482

    Article  MATH  MathSciNet  Google Scholar 

  2. Liberzon D. Switching in Systems and Control. Boston: Birkhauser, 2003

    MATH  Google Scholar 

  3. Sun Z D, Ge S S. Switched Linear Systems-Control and Design. New York: Springer-Verlag, 2004

    Google Scholar 

  4. Zhao J, Spong M W. Hybrid control for global stabilization of the cart-pendulum system. Automatica, 2001, 37: 1941–1951

    Article  MATH  MathSciNet  Google Scholar 

  5. Hespanha J P, Liberzon D, Angeli D, et al. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans Autom Contr, 2005, 50: 154–168

    Article  MathSciNet  Google Scholar 

  6. Zhai G S, Hu B, Yasuda K, et al. Disturbance attenuation properties of time-controlled switched systems. J Franklin Institute, 2001, 338: 765–779

    Article  MATH  MathSciNet  Google Scholar 

  7. Lin H, Zhai G S, Antsaklis P J. Robust stability and disturbance attenuation analysis of a class of networked control systems. In: IEEE Conference on Decision and Control, Maui, Hawaii, 2003. 2: 1182–1187

    Google Scholar 

  8. Gu K, Kharitonov V, Chen J. Stability of Time-Delay Systems. Boston, MA: Birkhauser, 2003

    MATH  Google Scholar 

  9. Richard J. Time-delay systems: an overview of some recent advances and open problems. Automatica, 2003, 39: 1667–1694

    Article  MATH  MathSciNet  Google Scholar 

  10. Fridman E, Shaked U. Delay-dependent stability and H ∞ control: constant and time-varying delays. Int J Contr, 2003, 76: 48–60

    Article  MATH  MathSciNet  Google Scholar 

  11. Han Q L, Gu K Q. On robust stability of time-delay systems with norm-bounded uncertainty. IEEE Trans Automat Contr, 2001, 46: 1426–1431

    Article  MATH  MathSciNet  Google Scholar 

  12. Gao H J, Wang C H. Delay-dependent robust and filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans Autom Contr, 2003, 48: 1661–1665

    Article  MathSciNet  Google Scholar 

  13. He Y, Wu M, She J H, et al, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Sys Contr Lett, 2004, 51: 57–65

    Article  MATH  MathSciNet  Google Scholar 

  14. He Y, Wu M, She J H, et al. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans Automat Contr, 2004, 49: 828–832

    Article  MathSciNet  Google Scholar 

  15. Xie G M, Wang L. Quadratic stability and stabilization of discrete-time switched systems with state delay. In: Proc 43rd IEEE Conf Decision and Control, Atlantis, Paradise Island, Bahamas, 2004. 3235–3240

  16. Sun X M, Zhao J, Hill D J. Stability and L 2-gain analysis for switched delay systems: a delay-dependent method. Automatica, 2006, 42: 1769–1774

    Article  MATH  MathSciNet  Google Scholar 

  17. Sun X M, Liu G P, Rees D, et al. Stability of systems with controller failure and time-varying delay. IEEE Trans Automat Contr, 2008, 53: 2391–2396

    Article  MathSciNet  Google Scholar 

  18. Sun Y G, Wang L, Guang G X. Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. Appl Math Comput, 2006, 180: 428–435

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Research Center of Information and Control, Dalian University of Technology, Dalian, 116024, China

    Yong Wang & Wei Wang

  2. Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, UK

    GuoPing Liu

  3. CTGT Center in Harbin Institute of Technology, Harbin, 150001, China

    GuoPing Liu

Authors
  1. Yong Wang
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  2. Wei Wang
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  3. GuoPing Liu
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Correspondence to Wei Wang.

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Wang, Y., Wang, W. & Liu, G. Stability of linear discrete switched systems with delays based on average dwell time method. Sci. China Inf. Sci. 53, 1216–1223 (2010). https://doi.org/10.1007/s11432-010-0115-8

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  • DOI: https://doi.org/10.1007/s11432-010-0115-8

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