Robust stabilization and H∞ control for uncertain discrete-time systems with time-varying delays

The problems of robust stabilization and H_∞ control for uncertain discrete-time systems with time-varying delays are investigated. Attention is focused on the design of a memoryless H_∞ state feedback controller such that the resulting closed-loop system is robustly exponentially stable with a prescribed level for all admissible uncertainties. A new delay-dependent sufficient condition for the existence of robust exponential H_∞ state feedback controllers is provided by constructing a new Lyapunov functional and introducing some slack matrix variables. The desired H_∞ controller can be obtained by solving a set of matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.