Second-order reciprocally convex approach to stability of systems with interval time-varying delays

Abstract

Recently, some triple integral terms in the Lyapunov Krasovskii functional have been introduced in the literature to reduce conservatism in the stability analysis of systems with interval time-varying delays. When we apply the Jensen inequality to partitioned double integral terms in the derivation of LMI conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters emerges. This paper proposes an efficient method to manipulate such a combination by extending the lower bound lemma. Some numerical examples are given to demonstrate the improvement of the proposed method. (C) 2013 Elsevier Inc. All rights reserved.