Finite‐time H ∞  control for discrete‐time switched nonlinear systems with time delay. (2nd December 2013)

• Record Type: Journal Article
• Authors: Zong, Guangdeng; Wang, Ruihua; Zheng, Weixing; Hou, Linlin
• Is Part Of: International journal of robust and nonlinear control. Volume 25:Number 6(2015)
• Page Start: 914
• Page End: 936
• Publication Date: 2013-12-02
• Subjects: Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3121
• Languages: English
• ISSNs: 1049-8923

Abstract

<abstract abstract-type="main" id="rnc3121-abs-0001"> <title>Summary</title> <p id="rnc3121-para-0001">In this paper, the problem of finite‐time <italic>H</italic>_∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of <italic>H</italic>_∞ 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 <italic>H</italic>_∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time <italic>H</italic>_∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time <italic>H</italic>_∞ 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 &amp; Sons, Ltd.</p> </abstract>