Robust Stability and Stabilization of Discrete Time-Delay System with Time-Varying Delay and Non-Linear Perturbations

In this paper, we consider the problems of robust stability and stabilization by static state feedback of discrete time-delay systems under non-linear perturbations. The delay in the system state may be time-varying. Firstly, by making use of some techniques, delay-dependent robust stability of the system is presented. Then, a sufficient condition on the existence of the state feedback controller is established in the terms of linear matrix inequality (LMI), which guarantee stability of the closed-loop system and at the same time maximize the nonlinearity bound. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.