A Lyapunov characterization of asymptotic controllability for nonlinear switched systems
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 1-11
https://doi.org/10.4134/BKMS.2014.51.1.1
Printed January 1, 2014
Yanling Wang and Ailing Qi
Tianjin University, Civil Aviation University of China
Abstract : In this paper, we show that general nonlinear switched systems are asymptotically controllable if and only if there exist control-Lyapunov functions for their relaxation systems. If the switching signal is dependent on the time, then the control-Lyapunov functions are continuous. And if the switching signal is dependent on the state, then the control-Lyapunov functions are $C^1$-smooth. We obtain the results from the viewpoint of control system theory. Our approach is based on the relaxation theorems of differential inclusions and the classic Lyapunov characterization.
Keywords : switched systems, control systems, asymptotically controllable, control-Lyapunov function, differential inclusions
MSC numbers : 34D20, 93B05, 93D05, 93D20
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