A new integral inequality for time-varying delay systems

This paper considers the delay-dependent stability analysis of time-varying delay systems. First of all, the previous Jensen´ s like inequality is firstly improved by a new inequality which has less conservatism according to our analysis. Another remarkable approach to reduce the conservatism of stability criteria is the delay-partitioning idea, and the advantage of this method provides larger delay bounds when the delay-partitioning number increases. These technical tools allow to construct efficiently a new class of Lyapunov-Krasovskii functional (LKF) in practice. Combining with the new inequality and reciprocal convex approach and some other inequality techniques, the new less conservative robust stability criteria are shown in form of linear matrix inequalities (LMIs). The effectiveness of the proposed results is illustrated by an example from the literature.