Stabilization control for discrete time systems with random delay

This paper is concerned with stabilization control problem for discrete time systems with random input delay. The random delay is not required to be less than a sampling interval as in previous works but it can vary in any range of finite length. By defining an appropriate stochastic variable, a random delayed system is converted into a multiplicative-noise stochastic system with multiple constant delays. It is noted that the multiplicative noises in the converted system are correlated at different time, which leads to a challenging difficulty of control because no available tool can be applied to such a system. By taking a new concept of F_k-d-1-measurable control, a necessary and sufficient condition to stabilize the random delayed system is given based on a coupled Riccati-type equation developed by the authors. Accordingly, the analytical stabilization controller is presented.