an:05869048
Zbl 1214.93043
Xiang, Weiming; Xiao, Jian
\(H_\infty\) finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance
EN
J. Franklin Inst. 348, No. 2, 331-352 (2011).
00274877
2011
j
93B36 93C10 93C55
finite-time stability; stabilization for switched nonlinear discrete-time systems; \(H_\infty\) finite-time boundedness; state feedback controller
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.