In this paper, we address the problems of robust H-infinity performance analysis and control synthesis for a class of discrete-time systems with norm-bounded parameter uncertainty and unknown constant state delay. Through finite-dimensional algebraic Riccati equations, we provide a necessary and sufficient condition for designing a memoryless state-feedback controller which stabilizes the discrete time-delay system under consideration and guarantees an H-infinity-norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. An example is worked out to illustrate the developed theory.