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${H}_{\infty }$ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. (English) Zbl 1214.93043
Summary: Finite-time stability concerns the boundedness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to ${H}_{\infty }$ finite-time boundedness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundedness, a state feedback controller is designed to ${H}_{\infty }$ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C10 Nonlinear control systems 93C55 Discrete-time control systems
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