This paper considers H-2/H-infinity, control problems involving discrete-time uncertain linear systems. The uncertain domain is supposed to be convex bounded, which naturally covers, as a particular case, the important class of interval matrices. The H-infinity guaranteed-cost control problem, solved for this class of uncertain systems, under no matching conditions, can be stated as follows : determine a state feedback gain (if one exists) such that the H-infinity norm of a given transfer function remains bounded by a prespecified level for all possible models. In the same context, problems on the determination of the smallest H-infinity upper bound and the minimization of an H-2 cost upper bound subject to H-infinity constraints are also addressed. The results follow from the fact that those problems are convex in the particular parametric space under consideration. Some examples illustrate the theory.