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Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

2013; Wiley; Volume: 25; Issue: 6 Linguagem: Inglês

10.1002/rnc.3121

1099-1239

Guangdeng Zong, Ruihua Wang, Wei Xing Zheng, Linlin Hou,

Adaptive Control of Nonlinear Systems

Summary In this paper, the problem of finite‐time H ∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H ∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H ∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H ∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H ∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.