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

This paper investigates the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay. Based on delay-central point method, the whole delay interval is divided into two equidistant subintervals at its central point and a new Lyapunov-Krasovskii (L-K) functionals which contains some triple-integral terms and augment terms are introduced on these intervals. Then, by using L-K stability theorem, integral inequality method and convex combination technique, a new delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities (LMIs). Unlike existing methodologies, when bounding the cross-terms that emerge 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 express the relationship of the correlative terms, so that it can reduce the complexity both in theoretical derivation and in computation. Finally, numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.