Exponential stability of uncertain discrete-time systems with state delay and input delay

This paper considers the robust control problem for a class of uncertain discrete-time systems with state delay and input delay. A sufficient condition is given for the robust exponential stability. A design strategy is then derived for memoryless state feedback control. One of the proofs makes use of Lyapunov-Krasovskii functional, and the condition is expressed in terms of linear matrix inequalities. All main results are illustrated with a numerical example.