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$L_{\infty}$ control with finite-time stability for switched systems under asynchronous switching. (English) Zbl 1264.93057
Summary: This paper is concerned with the problem of controller design for switched systems under asynchronous switching with exogenous disturbances. The attention is focused on designing the feedback controller that guarantees the finite-time bounded and $L_{\infty}$ finite-time stability of the dynamic system. Firstly, when there exists asynchronous switching between the controller and the system, a sufficient condition for the existence of stabilizing switching law for the addressed switched system is derived. It is proved that the switched system is finite-time stabilizable under asynchronous switching satisfying the average dwell-time condition. Furthermore, the problem of $L_{\infty}$ control for switched systems under asynchronous switching is also investigated. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
##### MSC:
 93B36 $H^\infty$-control 93D05 Lyapunov and other classical stabilities of control systems 93C30 Control systems governed by other functional relations
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