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Zbl 1214.93043
Xiang, Weiming; Xiao, Jian
$H_\infty$ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. (English)
[J] J. Franklin Inst. 348, No. 2, 331-352 (2011). ISSN 0016-0032; ISSN 1879-2693/e

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 2000:: *93B36 $H^\infty$-control
93C10 Nonlinear control systems
93C55 Discrete-time control systems

Keywords: finite-time stability; stabilization for switched nonlinear discrete-time systems; $H_\infty$ finite-time boundedness; state feedback controller

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Zentralblatt MATH Berlin [Germany]