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 linear discrete time-delayed systems with time-varying delays. At first, applying Lyapunov-Krasovskii functional method, sufficient condition for checking the stability of system is offered. Then, the stabilization of system is improved via dynamic state-feedback controller. In fact, the proposed condition is a criterion which results in increase of regions of stabilization for such systems. This result is in the linear matrix inequality (LMI) framework which can be solved easily by using the existing standard numerical software. Illustrative examples confirm the advantages of developed approach. In the sequel, the obtained stability and stabilization conditions will be extended to uncertain discrete time-delayed systems (UDTDS) with norm-bounded parameter uncertainties.