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

• Published in: International journal of robust and nonlinear control Vol. 25; no. 6; pp. 914 - 936
• Main Authors: Zong, Guangdeng, Wang, Ruihua, Zheng, Weixing, Hou, Linlin
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.04.2015; Wiley Subscription Services, Inc
• Subjects: average dwell time; delay-dependent stability conditions; finite-time boundedness; H ∞ control; Switched delay systems
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3121

SummaryIn 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.