Stabilization of Discrete-Time Delayed Systems via Partially Delay-Dependent Controllers

This paper is concerned with the stabilization problem for a class of discrete-time delayed systems, whose stabilizing controller is firstly designed to be partially delay-dependent. The distribution property of such a controller is firstly described by a discrete-time Markov chain with two modes. It is seen that two traditionally special cases of state feedback controller without or with time delay, respectively, are included. Based on the proposed controller, new stabilization conditions depending on some probabilities are developed. Because of the established results with LMI forms, they are further extended to more general cases that the transition probabilities are uncertain and totally unknown, while more applications are also given in detail. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.