Robust exponential stability of impulsive switched systems with switching delays: A Razumikhin approach

Abstract In this paper, we focus on the robust exponential stability of a class of uncertain nonlinear impulsive switched systems with switching delays. We introduce a novel type of piecewise Lyapunov–Razumikhin functions. Such functions can efficiently eliminate the impulsive and switching jump of adjacent Lyapunov functions at impulsive switching instants. By Razumikhin technique, the delay-independent criteria of exponential stability are established on the minimum dwell time. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained theoretical results.

[1]  Xingwen Liu,et al.  Stability Analysis of Switched Positive Systems: A Switched Linear Copositive Lyapunov Function Method , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Wassim M. Haddad,et al.  Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control , 2006 .

[3]  Yubin Liu,et al.  Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay , 2009, Math. Comput. Model..

[4]  Xinzhi Liu,et al.  Stability and robustness of quasi-linear impulsive hybrid systems☆ , 2003 .

[5]  David J. Hill,et al.  Comparison Principle and Stability of Discrete-Time Impulsive Hybrid Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[7]  Xinzhi Liu,et al.  Delay independent stability criteria of impulsive switched systems with time-invariant delays , 2008, Math. Comput. Model..

[8]  Shengyuan Xu,et al.  Robust H∞ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach , 2008 .

[9]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[10]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[11]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[12]  Chuandong Li,et al.  Hybrid impulsive and switching time-delay systems , 2009 .

[13]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[14]  Zhigang Zhang,et al.  Robust H∞ control of a class of discrete impulsive switched systems , 2009 .

[15]  Kok Lay Teo,et al.  Exponential Stability With $L_{2}$-Gain Condition of Nonlinear Impulsive Switched Systems , 2010, IEEE Transactions on Automatic Control.

[16]  Xinzhi Liu,et al.  Input-to-state stability of impulsive and switching hybrid systems with time-delay , 2011, Autom..

[17]  Wei Zhu,et al.  Stability analysis of impulsive switched systems with time delays , 2009, Math. Comput. Model..