Robust Stochastic Stabilization of Uncertain Stochastic Jump Systems with Time-Varying Delays

This paper studies the problem of robustly stochastic stability of uncertain stochastic systems with time-varying delays, where the system is subjected to both Brownian motion and Markovian parameter jumping. By using some zero equations, neither model transformation nor bounding for cross terms is required to obtain the delay-dependent results. The problem of robustly stochastic stability addressed in this paper is to design a state feedback controller such that, for all admissible uncertainties, the closed-loop system is robustly stochastically stable. A criterion for the existence of such controller is derived based on the Lyapunov function combined with linear matrix inequalities (LMI).