Stabilization of discrete time-delay systems with parametric uncertainty

In this paper, the problem of memoryless static state feedback control for a class of discrete-time uncertain systems with delayed state is considered. The uncertain time-delay system under consideration is described by state difference equation with time-varying unknown, norm-bounded parameter uncertainty. Necessary and sufficient condition for the existence of the desired control law is provided. Based on the discrete Lyapunov functional technique combined with linear matrix inequality (LMI) approach, a new design method is proposed for synthesizing robust control laws for the uncertain discrete time-delay systems. It is shown that the construction of the stabilizing controller involves solving a certain LMI.