Stability of Interval Time-Varying Delay Systems: A Nonuniform Delay Partitioning Approach

Abstract

This paper investigates the conservatism reduction of Lyapunov-Krasovskii based conditions for the stability of a class of interval time-varying delay systems. The main idea is based on the nonuniform decomposition of the integral terms of the Lyapunov-Krasovskii functional. The delay interval is decomposed into a finite number of nonuniform segments with some scaling parameters. Both differentiable delay case and nondifferentiable delay case or unknown delay derivative bound case are taken into consideration. Sufficient delay-dependent stability criteria are derived in terms of matrix inequalities. Introducing a cone complementary problem, a convex optimization algorithm is obtained so that a suboptimal maximum allowable delay upper bound is achieved. Two numerical examples with case studies are given to demonstrate the effectiveness of the proposed method with respect to some existing ones from the literature.