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

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 4, 2012, Pages 1805-1812

  Liu, Xiu ^a   Zhong, Shouming ^a   Ding, Xiuyong ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Exponential stability; Impulsive systems; Minimum dwell time; Razumikhin method; Switched systems

Indexed keywords

ASYMPTOTIC STABILITY; IMPULSE RESPONSE; STABILITY CRITERIA; SWITCHING; SYSTEM STABILITY;

IMPULSIVE SYSTEMS; LYAPUNOV'S FUNCTIONS; LYAPUNOV-RAZUMIKHIN FUNCTIONS; MINIMUM DWELL TIME; PIECE-WISE; RAZUMIKHIN METHOD; ROBUST EXPONENTIAL STABILITY; SWITCHED SYSTEM; SWITCHING DELAY; SWITCHING INSTANTS;

LYAPUNOV FUNCTIONS;

EID: 80054975935     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.09.013     Document Type: Article

References (17)

1. Haddad W.M., Chellaboina V., Nersesov S.G. Impulsive and hybrid dynamical systems: stability, dissipativity, and control 2006, Princeton University Press, Princeton.
2. Bainov D.D., Simeonov P.S. Systems with impulse effect: stability, theory and applications 1989, Halsted Press, New York.
3. Liberzon D. Switching in systems and control 2003, Birkhäuser, Boston.
4. Liu X. Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method. IEEE Trans Circuits Syst Expr Briefs 2009, 56(5):414-418.
5. Lakshmikantham V., Bai{dotless}̌nov D., Simeonov P. Theory of impulsive differential equations 1989, World Scientific, Teaneck, NJ.
6. Li C., Ma F., Feng G. Hybrid impulsive and switching time-delay systems. IET Control Theor Appl 2009, 3(11):1487-1498.
7. Liu Y., Feng W. Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay. Math Comput Model 2009, 49:249-264.
8. Xu H., Liu X., Teo K. Delay independent stability criteria of impulsive switched systems with time-invariant delays. Math Comput Model 2008, 47:372-379.
9. ∞ stabilization for uncertain switched impulsive control systems with state delay: an LMI approach. Nonlinear Anal Hybrid Syst 2008, 2:1287-1300.
10. Liu B., Liu X., Liao X. Stability and robustness of quasi-linear impulsive hybrid systems. J Math Anal Appl 2003, 283:416-430.
11. Liu J., Liu X., Xie W. Input-to-state stability of impulsive and switching hybrid systems with time-delay. Automatica 2011, 45(5):899-908.
12. Guan Z., Hill D., Shen X.S. On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans Automat Contr 2005, 50(7):1058-1062.
13. 2-gain condition of nonlinear impulsive switched systems. IEEE Trans Automat Contr 2010, 55(10):2429-2433.
14. Yang C., Zhu W. Stability analysis of impulsive switched systems with time delays. Math Comput Model 2009, 50:1188-1194.
15. ∞ control of a class of discrete impulsive switched systems. Nonlinear Anal Theor Meth Appl 2009, 71:e2790-e2796.
16. Liu B., Hill D. Comparison principle and stability of discrete-time impulsive hybrid systems. IEEE Trans Circuits Syst Regul Pap 2009, 56(1):233-245.
17. Li X., Souza C.E. Criteria for robust stability and stabilization of uncertain linear system with state delay. Automatica 1997, 33:1657-1662.