Stabilizing Control of A Class of Discrete-Time Systems with Random Delay

This paper investigate the stabilizing controller design of a class of linear time-invariant systems with one-step random delay in discrete time. Both stabilizing dynamic feedback and state feedback control are in consideration. The dynamic stabilizing controller of the closed-loop stochastic system are determined by the solutions of two discrete algebraic Riccati equations (DAREs). And the state feedback problem is converted into a static output feedback (SOF) problem. Two theorems are provided that guarantee the existence of controllers which stabilize the closed-loop system in the sense of mean-square. In addition, all stabilizing controllers are given by means of parametrization.