Mean-square stabilization for stochastic systems with multiple delays

This paper is concerned with the mean-square stabilization problem for the stochastic systems with multiple delays. The stabilizing controller is given in terms of the modified algebraic Riccati equation. There are two key points in our arguments. The first one is to reduce the original system with multiple delays to one delay-free stochastic system. Note that the current state feedback controller is infeasible to the reduced system for the involvement of the past noise information. Our second key point is to design a novel controller in the feedback form of the conditional expectation.