A LYAPUNOV CHARACTERIZATION OF ASYMPTOTIC CONTROLLABILITY FOR NONLINEAR SWITCHED SYSTEMS

Title & Authors
A LYAPUNOV CHARACTERIZATION OF ASYMPTOTIC CONTROLLABILITY FOR NONLINEAR SWITCHED SYSTEMS
Wang, Yanling; Qi, Ailing;

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 $\small{C^1}$-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;
Language
English
Cited by
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