This paper considers \(H_2/H_\infty\) control problems involving discrete-time uncertain linear systems. The uncertain domain is supposed to be convex bounded, which naturally contains, as a particular case, the important class of interval matrices. The \(H_\infty\) 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 it exists) such that the \(H_\infty\) 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 \(H_\infty\) upper bound and the minimization of an \(H_2\) cost upper bound subject to \(H_\infty\) constraints are also addressed. The results follow from the fact that these problems are convex in the particular parametric space under consideration. Some examples illustrate the theory.