H∞ Control for Multi-time-delay Uncertain Discrete Systems

This paper studies the problems of quadratic stabilization and H∞ control for a class of multi-time-delay uncertain discrete systems. Suppose that the time-varying uncertain parameters are norm-bounded, but not required to satisfy strict matched conditions, state and input for the system are both with multi-time-delay. New sufficient conditions of quadratic stabilization and H∞ control are given for the system by generalized Lyapunov function and linear matrix inequalities. In terms of linear matrix inequalities, H∞ controller can be obtained and a prescribed H∞ performance lever of the closed-loop system has an upper bound for all admissible parameters uncertainties. Furthermore, the optimal H∞ robust control law can be obtained by solving some convex optimization problems. A numerical example is offered to show the potential of the proposed techniques.