Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

This paper presents necessary and sufficient conditions for quadratic stability and stabilization of uncertain linear discrete systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. The results are obtained in terms of linear matrix inequality. A robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities. Our results can be regarded as extensions of existing results on quadratic stability and stabilization for discrete-time delay systems with uncertainties. Two examples are presented to demonstrate the effectiveness of the proposed approach.