Robust stabilization of discrete-time systems with time-varying delays

This paper introduces a new approach to robust stabilization of discrete-time delay systems under non-linear perturbations. For the discrete-time systems with state/input delays, the robust stabilization problem is transformed to a constrained convex optimization one. Sufficient conditions on the existence of state feedback controllers are established in terms of linear matrix inequality (LMI), which guarantee stability of the closed-loop system and at the same time maximize the non-linearity bound. Finally, numerical examples are presented to illustrate the efficiency and feasibility of our proposed approach.