Delay-dependent stability criteria for interval time-varying delay systems with nonuniform delay partitioning approach

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 and unknown delay derivative bound case are taken into consideration. Sufficient delay-dependent stability criteria are derived in terms of matrix inequalities. Two suboptimal delay fractionation schemes, namely, linearization with cone complementary technique and linearization under additional constraints are introduced in order to find a feasible solution set using LMI solvers with a convex optimization algorithm so that a suboptimal maximum allowable delay upper bound is achieved. It is theoretically demonstrated that the proposed technique has reduced complexity in comparison to some existing delay fractionation methods from the literature. A numerical example with case studies is given to demonstrate the effectiveness of the proposed method with respect to some existing ones from the literature.