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Finite-time stability of switched nonlinear systems with finite-time unstable subsystems. (English) Zbl 1307.93192
Summary: Up to now, the precondition that each subsystem should be finite-time stable or finite-time bounded is potentially assumed in most existing results for finite-time stability and finite-time boundedness of switched systems. If one subsystem of switched systems is not finite-time stable or finite-time bounded, the previous results may not work. In this paper, based on Lyapunov-like functions, finite-time stability and finite-time boundedness problems of switched nonlinear systems with subsystems that are not finite-time stable or finite-time bounded are discussed. Sufficient conditions are given under which switched nonlinear systems with subsystems that are finite-time unstable or finite-time unbounded are guaranteed to be still finite-time stable or finite-time bounded by virtue of Lyapunov-like functions respectively. The results also show the effect of switching signals and the total dwell time of finite-time unstable or finite-time unbounded subsystems on finite-time stability and finite-time boundedness of switched nonlinear systems. Numerical examples are employed to verify the efficiency of the proposed method.

##### MSC:
 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93C10 Nonlinear systems in control theory 93D30 Lyapunov and storage functions 93D99 Stability of control systems
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