Skip to main content
SpringerLink
Log in

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, the input-to-state stability (ISS) analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hespanha J P, Uniform stability of switched linear systems extensions of Lasalles invariance principle, IEEE Transactions on Automatic Control, 2004, 49(4): 470–482.

    Article  MathSciNet  MATH  Google Scholar 

  2. Johansson M and Rantzer A, Computation of piecewise quadratic Lyapunov functions for hybrid systems, IEEE Transactions on Automatic Control, 1998, 43(4): 555–559.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ren H L, Zong G D, Hou L L, et al., Finite-time control of interconnected impulsive switched systems with time-varying delay, Applied Mathematics and Computation, 2016, 276(4): 143–157.

    Article  MathSciNet  Google Scholar 

  4. Lu B, Wu F, and Kim S, Switching LPV control of an F-16 aircraft via controller state reset, IEEE Transactions on Control Systems Technology, 2006, 14(2): 267–277.

    Article  Google Scholar 

  5. Morse A S, Supervisory control of families of linear set-point controllers part I: Exact matching, IEEE Transactions on Automatic Control, 1996, 41(10): 1413–1431.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gu K, Chen J, and Kharitonov V L, Stability of Time-Delay Systems, Springer Science & Business Media, 2003.

    Book  MATH  Google Scholar 

  7. Zong G D, Wang R H, Zheng W X, et al., Finite time stabilization for a class of switched time-delay systems under asynchronous switching, Applied Mathematics and Computation, 2013, 219(11): 5757–5771.

    Article  MathSciNet  MATH  Google Scholar 

  8. Sun X M, Liu G P, Wang W, et al., Stability analysis for networked control systems based on event-time-driven mode, International Journal of Control, 2009, 82(12): 2260–2266.

    Article  MathSciNet  MATH  Google Scholar 

  9. Saldivar B, Mondie S, Loiseau J J, et al., Exponential stability analysis of the drilling system described by a switched neutral type delay equation with nonlinear perturbations, 50th IEEE Conference on Decision and Control and European Control Conference, 2011, 4164–4169.

    Chapter  Google Scholar 

  10. Haimovich H and Seron M M, Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations, Automatica, 2013, 49(3): 748–754.

    Article  MathSciNet  MATH  Google Scholar 

  11. Wu L and Zheng W X, Weighted H ∞ model reduction for linear switched systems with timevarying delay, Automatica, 2009, 45(1): 186–193.

    Article  MathSciNet  Google Scholar 

  12. Lian J, Shi P, and Feng Z, Passivity and passification for a class of uncertain switched stochastic time-delay systems, IEEE Transactions Cybernetics, 2013, 43(1): 3–13.

    Article  Google Scholar 

  13. Zong G D, Xu S Y, and Wu Y Q, Robust H-infinity stabilization for uncertain switched impulsive control systems with state delay an LMI approach, Nonlinear Analysis: Hybrid Systems, 2008, 2(4): 1287–1300.

    Article  MathSciNet  MATH  Google Scholar 

  14. Vu L, Chatterjeee D, and Liberzon D, Input-to-state stability of switched systems and switching adaptive control, Automatica, 2007, 43(4): 639–646.

    Article  MathSciNet  MATH  Google Scholar 

  15. Shen M and Ye D, Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions, Fuzzy Sets and Systems, 2013, 217(16): 80–95.

    Article  MathSciNet  MATH  Google Scholar 

  16. Sontag E D, Smooth stabilization implies coprime factorizatio, IEEE Transactions on Automatic Control, 1989, 34(4): 435–443.

    Article  MathSciNet  MATH  Google Scholar 

  17. Sontag E D and Wang Y, New characterizations of input-to-tate stability, IEEE Transactions on Automatic Control, 1996, 41(9): 1283–1294.

    Article  MathSciNet  MATH  Google Scholar 

  18. Sontag E D and Wang Y, On characterizations of the input-to-state stability property, Systems and Control Letters, 1995, 24(5): 351–359.

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu J, Liu X, and Xie W C, Input-to-state stability of impulsive and switching hybrid systems with time-delay, Automatica, 2011, 47(5): 899–908.

    Article  MathSciNet  MATH  Google Scholar 

  20. Sun X M and Wang W, Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics, Automatica, 2012, 48(9): 2359–2364.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang Y E, Sun X M, Shi P, et al., Input-to-state stability of switched nonlinear systems with time delays under asynchronous switching, IEEE Transactions Cybernetics, 2013, 43(6): 2261–2265.

    Article  Google Scholar 

  22. Ning C Y, He Y, Wu M, et al., Input-to-state stability of nonlinear systems based on an indefinite Lyapunov function, Systems and Control Letters, 2012, 61(12): 1254–1259.

    Article  MathSciNet  MATH  Google Scholar 

  23. Zong G D, Wang R H, Zheng W X, et al., Finite-time H ∞ control for discrete-time switched nonlinear systems with time delay, International Journal of Robust and Nonlinear Control, 2015, 25(6): 914–936.

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang Y E, Sun X M, and Zhao J, Stabilization of a class of switched stochastic systems with time delays under asynchronous switching, Circuits, Systems, and Signal Processing, 2013, 32(1): 347–360.

    Article  MathSciNet  Google Scholar 

  25. Zong G D, Ren H L, and Hou L L, Finite-time stability of interconnected impulsive switched systems, IET Control Theory and Applications, 2016, 10(6): 648–654.

    Article  MathSciNet  Google Scholar 

  26. Xie W X, Wen C Y, and Li Z G, Input-to-state stabilization of switched nonlinear systems, IEEE Transactions on Automatic Control, 2001, 46(7): 1111–1116.

    Article  MathSciNet  MATH  Google Scholar 

  27. Xie G M and Wang L, Stabilization of switched linear systems with time-delay in detection of switching signal, Journal of Mathematical Analysis and Applications, 2005, 305(1): 277–290.

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhou B and Luo W, Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems, arXiv:1607.02217, 2016.

  29. Chen G and Yang Y, Relaxed conditions for the input-to-State stability of switched nonlinear time-varying systems, IEEE Transactions on Automatic Control, 2017, 62(9): 4706–4712.

    Article  MathSciNet  Google Scholar 

  30. Wang Y E, Sun X M, Wang W, et al., Stability properties of switched nonlinear delay systems with synchronous or asynchronous switching, Asian Journal of Control, 2015, 17(4): 1–9.

    MathSciNet  MATH  Google Scholar 

  31. Vu L and Morgansen K A, Stability of time-delay feedback switched linear systems, IEEE Transactions on Automatic Control, 2010, 55(10): 2385–2389.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, China

    Guangdeng Zong & Haijuan Zhao

Authors
  1. Guangdeng Zong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haijuan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haijuan Zhao.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61773235, 61273123, 61374004, 61403227, and in part by Program for New Century Excellent Talents in University under Grant No. NCET-13-0878, and in part by the Taishan Scholar Project of Shandong Province of China under Grant No. tsqn20161033.

This paper was recommended for publication by Editor SUN Jian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zong, G., Zhao, H. Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method. J Syst Sci Complex 31, 875–888 (2018). https://doi.org/10.1007/s11424-018-6237-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-018-6237-6

Keywords

Search

Navigation