Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition

Abstract

This paper studies the problem of robustly stochastic stability and stabilization for a class of uncertain Markov jump linear systems with time delay. A new stochastic Lyapunov–Krasovskii functional (LKF) is constructed for the stability analysis and stabilization, in which the delay is uniformly divided into multiple segments. Based on this LKF and using an improved Jensen's integral inequality, the improved delay-dependent stochastic stability criteria are first derived in terms of linear matrix inequalities (LMIs). Then, an LMI approach to the design of stabilizing controllers via delayed state feedback is developed. The previous stability criteria are extended to give the delay-dependent stabilization conditions in terms of LMIs. Furthermore, an LMI optimization algorithm is proposed to find the maximum allowable delay of the system. Finally, numerical examples show that the proposed results are effective and much less conservative than some existing results.