Stabilization for Stochastic Discrete-Time Systems with Multiplicative Noise and Multiple Input Delay

This paper focuses on the stabilization problem of discrete-time systems with multiple input delay and multiplicative noise in both state and control channel. By designing the cost function and exploring the property of the cost function in the stochastic setting, the stabilization condition is obtained based on receding horizon control. It is shown that the system can be stabilized in the mean square sense if two terminal weighting matrices satisfy the proposed linear matrix inequality. The explicit stabilizing controller is obtained by solving the coupled difference equation. A numerical example illustrates the effectiveness of the proposed method.