Abstract: This paper is concerned with the problem of full-order robust l2-l∞ filtering for uncertain discrete-time systems with a single delay in the state. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain, entering into all the matrices of the system state-space model. Sufficient conditions are established in terms of linear matrix inequalities for the existence of filters guaranteeing a prescribed energy-to-peak disturbance attenuation level for all possible uncertainties and time delays. And the admissible filter can be found by solving a convex optimization problem with global convergence assured. A numerical example demonstrates the validity of the proposed filter design procedure.