Abstract: This paper deals with the problem of guaranteed cost and H^∞ disturbance attenuation during the robust asymptotic stabilization period of a class of uncertain discrete time-delay systems. Based on Lyapunov stability theory and the linear matrix inequalities (LMI) approach, a sufficient condition is presented for the existence of guaranteed cost H^∞ state feedback controllers. By solving a certain linear matrix inequality, the guaranteed cost H^∞ control laws are obtained. A numeric example is given to demonstrate the effectiveness and superiority of the designing method.

Key words: linear matrix inequalities, uncertainty, discrete time-delay systems, guaranteed cost control, H^∞ control