Stabilization analysis for discrete-time systems with time delay

The stabilization problem for a class of discrete-time systems with time-varying delay is investigated. By constructing an augmented Lyapunov function, some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality (LMI) technique. When norm-bounded parameter uncertainties appear in the delayed discrete-time system, a delay-dependent robust exponential stabilization criterion is also presented. All of the criteria obtained in this paper are strict linear matrix inequality conditions, which make the controller gain matrix can be solved directly. Three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results.