New bounded real lemma representations for time-delay systems and their applications

Abstract

Abstract—New delay-dependent/delay-independent bounded real criteria are derived for linear continuous-time systems with delay in the dynamics and in the objective function. A sufficient condition for the system to possess a-norm that is less than a prescribed level, is given in terms of a linear matrix inequality (LMI). The proposed criteria are less conservative than other existing criteria since they are based on an augmented model that is equivalent to the original system and since they require bounds for fewer terms. We apply the new bounded real criteria to state-feedback control. The advantage of the new criteria is demonstrated by four examples. The first two compare our results with those obtained in the literature for the bounded real lemma and the other two examples treat the state-feedback control problem and compare our result with recently published designs. Index Terms—Bounded real lemma, delay-dependent criteria,-state-feedback control, linear matrix inequalities (LMIs), time-delay systems. I