Robust H∞ control for uncertain stochastic systems with state delay

This note deals with the problems of robust stochastic stabilization and robust H ∞ control for uncertain stochastic systems with a time-varying delay in the state. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both the state and input matrices. The purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H ∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H ∞ performance is required to be achieved. In terms of a linear matrix inequality, sufficient conditions for the solvability of these problems are proposed respectively; the expressions of desired state feedback controllers are given. An example illustrating the proposed approach is provided.