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Bull. Korean Math. Soc. 2014; 51(1): 1-11
Printed January 1, 2014
https://doi.org/10.4134/BKMS.2014.51.1.1
Copyright © The Korean Mathematical Society.
A Lyapunov characterization of asymptotic controllability for nonlinear switched systems
Yanling Wang and Ailing Qi
Tianjin University, Civil Aviation University of China
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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