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An improved characterization of bounded realness for singular delay systems and its applications
Author(s) -
Xu Shengyuan,
Lam James,
Zou Yun
Publication year - 2008
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.1215
Subject(s) - bounding overwatch , bounded function , control theory (sociology) , impulse (physics) , mathematics , upper and lower bounds , lemma (botany) , linear matrix inequality , computer science , mathematical optimization , mathematical analysis , control (management) , ecology , physics , poaceae , quantum mechanics , artificial intelligence , biology
Abstract This paper is concerned with establishing a delay‐dependent bounded real lemma (BRL) for singular systems with a time delay. Without resorting to any bounding techniques for some cross terms and model transformation, a new version of BRL for such systems is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H ∞ performance level for any delays smaller than a given upper bound. Based on this, an H ∞ state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as H ∞ results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.