An improved characterization of bounded realness for singular delay systems and its applications

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.