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An improved characterization of bounded realness for singular delay systems and its applications. (English) Zbl 1284.93117
Summary: 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 \(H_{\infty }\) performance level for any delays smaller than a given upper bound. Based on this, an \(H_{\infty }\) state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as \(H_{\infty }\) results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
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