Abstract: This paper deals with the problem of H^∞ control for linear discrete systems with multiple state delays. Based on-linear matrix inequalities, a sufficient condition is presented for the systems to be H^∞ state feedback stabilizable. By solving a certain linear matrix inequality, the H^∞ controllers are obtained. A numeric example is given to demonstrate the effectiveness and superiority of the design method.

Key words: time-delay, linear matrix inequalities (LMI), H^∞ control, discrete systems