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.
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Hespanha J P, Uniform stability of switched linear systems extensions of Lasalles invariance principle, IEEE Transactions on Automatic Control, 2004, 49(4): 470–482.
Johansson M and Rantzer A, Computation of piecewise quadratic Lyapunov functions for hybrid systems, IEEE Transactions on Automatic Control, 1998, 43(4): 555–559.
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.
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.
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.
Gu K, Chen J, and Kharitonov V L, Stability of Time-Delay Systems, Springer Science & Business Media, 2003.
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.
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.
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.
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.
Wu L and Zheng W X, Weighted H ∞ model reduction for linear switched systems with timevarying delay, Automatica, 2009, 45(1): 186–193.
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.
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.
Vu L, Chatterjeee D, and Liberzon D, Input-to-state stability of switched systems and switching adaptive control, Automatica, 2007, 43(4): 639–646.
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.
Sontag E D, Smooth stabilization implies coprime factorizatio, IEEE Transactions on Automatic Control, 1989, 34(4): 435–443.
Sontag E D and Wang Y, New characterizations of input-to-tate stability, IEEE Transactions on Automatic Control, 1996, 41(9): 1283–1294.
Sontag E D and Wang Y, On characterizations of the input-to-state stability property, Systems and Control Letters, 1995, 24(5): 351–359.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Zhou B and Luo W, Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems, arXiv:1607.02217, 2016.
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.
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.
Vu L and Morgansen K A, Stability of time-delay feedback switched linear systems, IEEE Transactions on Automatic Control, 2010, 55(10): 2385–2389.
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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.
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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
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DOI: https://doi.org/10.1007/s11424-018-6237-6