New Lyapunov-Krasovskii stability condition for uncertain systems with interval time-varying delays

Abstract

This paper investigates the problem of robust stability for a class of linear uncertain system with interval time-varying delay. Based on delay-central point method and by means of L-K stability theorem, integral inequality method and convex combination technique, a new delay-dependent stability criterion for the system is formulated in terms of linear matrix inequalities (LMIs). Unlike existing methods, when bounding the cross-terms that emerged from the time derivative of the L-K functional, neither superfluous free weighting matrices are introduced nor any useful terms are neglected, only using tighter integral inequalities and a very few free weighting matrices for expressing the relationship of the correlative terms, so that it can reduce the complexity both in theoretical derivation and in computation. As a result, it is effective to reduce the conservatism of the results. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method.