Exponential Stabilization for Ito Stochastic Systems with Multiple Input Delays

TL;DR

This paper addresses the stabilization of Ito stochastic systems with multiple delays and noise, providing necessary and sufficient conditions via Riccati equations, and introduces a novel feedback controller based on conditional expectation.

Contribution

It introduces a new approach to stabilize Ito systems with multiple delays using modified Riccati equations and a feedback controller based on conditional expectation.

Findings

Derived solvability conditions for the modified Riccati equation.

Established mean-square exponential stabilization criteria.

Proposed a novel feedback controller based on the conditional expectation.

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.