Novel Stabilization and Robust Stabilization Conditions for Linear Discrete Time-Delayed Systems

In this paper, the problems of stability and stabilization will be discussed for discrete time-delayed systems (DTDS) with time-varying delays. At first, applying discretetime Lyapunov–Krasovskii functional method, sufficient condition for checking the global asymptotic stability (GAS) of time-delayed system is offered. Then, the stabilization of system is improved via dynamic state-feedback controller (DSFC). This result is in the linear matrix inequality (LMI) framework which can be solved easily by using the existing standard numerical software. By comparison and with respect to some previous results, the novelty of our proposed approach is less conservative of the obtained stabilization regions for this class of linear systems. Illustrative examples are given to confirm the advantages of developed stabilization condition over the similar cases that are reported in the different references. In the sequel, the obtained results, including stability analysis and dynamic state feedback stabilization are further extended to uncertain discrete time-delayed systems (UDTDS) with normbounded parameter uncertainties.