Guaranteed cost D-stabilization and H∞ D-stabilization for linear discrete time-delay systems

The problems of robust guaranteed cost D-stabilization and H∞ D-stabilization are investigated in this paper for linear discrete time-delay systems. Under the framework of direct approach, sufficient conditions of robust guaranteed cost D-stability and H∞ D-stability are proposed in terms of linear matrix inequality (LMI) respectively. Furthermore, design methods of optimal guaranteed cost D-stabilization controller and optimal H∞ D-stabilization controller are given. The controllers not only guarantee that all poles of the closed-loop system remain inside the specified disk D(α,r), but also minimize the quadratic performance index (for the case of guaranteed cost D-stabilization) or the exogenous disturbance attenuation level (for the case of H∞ D-stabilization). Numerical examples are provided to illustrate the effectiveness of the proposed methods.