New stability criteria for linear systems with interval time-varying delays via an extended state vector

This paper considers the stability problem of time-delayed system with interval time-varying delays. Based on a new Lyapunov-Krasovskii functional, improved stability criteria are derived in terms of linear matrix inequalities(LMIs). By efficiently applying Jensen inequality lemma, the lower bound lemma for reciprocal convexity, and Wirtinger-based integral inequality lemma, the tighter upper bound of the derivative of the proposed Lyapunov-Krasovskii functional is obtained. A numerical examples show the effectiveness of the proposed approaches by comparison of the maximum delay bounds.