Predictor Feedback Stabilization of Stochastic Linear Delayed Systems with Both Additive and Multiplicative Noises

Abstract

In this paper we investigate memory control of stochastic linear delayed systems with both additive and multiplicative noises. A new formula is first presented to obtain the prediction vector from the system dynamics and then it is used for feedback to reduce the input delay in the original delayed system. To ensure the stability of closed-loop system, some matrix inequality conditions are given that in the case of feasibility provide the stabilizing gain of the predictor controller. The proposed method is applied to stochastic quarter-car model of an active suspension system to show the effectiveness of the approach.