H∞ tracking of uncertain stochastic time-delay systems: Memory state-feedback controller design

The problem of state robust H∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov-Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods.