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A µ‐dependent approach to H ∞ control of uncertain switched linear systems with average dwell time
Author(s) -
Zhang Lixian,
Boukas ElKebir,
Shi Peng,
Chen Zhaobo
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.919
Subject(s) - dwell time , control theory (sociology) , controller (irrigation) , exponential stability , mathematics , discrete time and continuous time , class (philosophy) , linear system , state (computer science) , full state feedback , stability (learning theory) , control (management) , computer science , nonlinear system , algorithm , mathematical analysis , physics , statistics , medicine , clinical psychology , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
This paper concerns H ∞ control problem for a class of discrete‐time uncertain switched linear systems with average dwell time. The stability result for general discrete‐time switched systems is first explored, and a µ‐dependent approach is then introduced for the considered systems to the H ∞ controller solution. A mode‐dependent state‐feedback controller is designed such that the resulting closed‐loop system is robust exponentially stable and has a prescribed exponential H ∞ performance index. The µ‐dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.