Exponential stability of switched systems with delay: A multiple lyapunov function approach

Zidonghua Xuebao/Acta Automatica Sinica

Volumn 33, Issue 9, 2007, Pages 985-988

  Cong, Shen ^a   Fei, Shu Min ^b   Li, Tao ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Exponential stability; Halanay inequality; Switched systems; Time delay

Indexed keywords

ASYMPTOTIC STABILITY; SWITCHING; TIME DELAY;

EXPONENTIAL STABILITY; HALANAY INEQUALITY; STATE DELAY; SWITCHED SYSTEMS;

LYAPUNOV FUNCTIONS;

EID: 35349018447     PISSN: 02544156     EISSN: None     Source Type: Journal    
DOI: 10.1360/aas-007-0985     Document Type: Article

References (12)

1. Hale J. Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
2. Blanchini F. Nonquadratic Lyapunov functions for robust control. Automatica, 1995, 31(3): 451-461.
3. Cong Shen, Fei Ji-Qing, Fei Shu-Min. Exponential stability of seconde-order switched systems. Control and Decision, 2006, 21(10): 1177-1180.
4. Lin H, Antsaklis P. A necessary and sufficient condition for robust asymptotic stabilizability of continuous time uncertain switched linear system. In: Proceedings of 43rd IEEE Conference on Decision and Control. IEEE, 2004, 4: 3690-3695.
5. Molchanov A P, Pyatnitsky Y S. Criteria of asymptotic stability of differentail and difference inclusions encountered in control theory. Systems and Control Letters, 1989, 13(1): 59-64.
6. Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.
7. Liberzon D, Morse A S. Basic problems in stability and design of switching system. IEEE Control Systems, 1999, 19(10): 59-70.
8. Liberzon D, Morse A S. Stability of switched systems with average dwell-time. In: Proceedings of 38th IEEE Conference on Decision and Control. IEEE, 1999. 2655-2660.
9. Pu Xi-Lin, Yan Bao-Qiang, Liu Yan-Sheng. Introduction to Impulsive Differential System. Beijing: Science Press, 2005.
10. Halanay A. Differential Equations: Stability, Oscilations, Time Lags. New York: Academic Press, 1966.
11. Filippov A V. Differential Equations with Discontinuous Right-hand Sides. Amsterdam: Kluwer Academic Press, 1988.
12. Pyatnitsky Y S, Rapoport L B. Criteria of asymptotic stability of differentail inclusions and periodic motions of time-varying nonlinear control systems. IEEE Transactions on Circuits and Systems-I, 1996, 43(3): 219-229.