Non-fragile Guaranteed-cost Robust H∞ control for Discrete Uncertain Time-delay System

This paper deals with a problem on non-fragile guaranteed cost and H_infin robust control for discrete uncertain system with state and input time-delay. Based on the linear matrices inequalities (LMIs) and Schur complements, First, we presented and proved a sufficient condition by a proper Lyapunov function such that the closed-loop system is robust stable, and satisfies H_infin norm bound and a given cost function has upper bound;Next, we designed a non-fragile guaranteed cost and H_infin robust controller such that the closed-loop system is regular impulse free and asymptotically stable, moreover, satisfies H_infin performance. The design method is given in terms of solving LMIs. Finally, a simple example is provided to demonstrate the effectiveness of the proposed approach.