Exponential Stabilization for Ito Stochastic Systems with Multiple Input Delays

Abstract

In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applications such as networked control systems. Sufficient and necessary conditions are obtained for the exponential stabilization problem of Ito stochastic systems with multiple delays. On one hand, we derive the solvability of the modified Riccati equation in case of the mean-square exponential stabilization. On the other hand, the mean-square exponential stabilization is guaranteed by the solvability of a modified Riccati equation. A novel stabilizing controller is shown in the feedback from of the conditional expectation in terms of the modified algebraic Riccati equation. The main technique is to reduce the original system with multiple delays to a pseudo delay-free system.