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Stability, L 2 ‐gain and asynchronous H ∞ control for continuous‐time switched systems
Author(s) -
Zhang Hongbin,
Wang Bo,
Xie Dehua,
Xu Shengyuan,
Dang Chuangyin
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3107
Subject(s) - asynchronous communication , dwell time , control theory (sociology) , exponential stability , stability (learning theory) , lyapunov function , mathematics , class (philosophy) , extension (predicate logic) , control (management) , computer science , nonlinear system , telecommunications , physics , medicine , clinical psychology , quantum mechanics , artificial intelligence , machine learning , programming language
Summary This paper is concerned with the stability and L 2 ‐gain problems for a class of continuous‐time linear switched systems with the existed asynchronous behaviors, where ‘asynchronous’ means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L 2 ‐gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H ∞ control. Based on the result, the mode‐dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd.