In this paper, the problem of determining the worst-case Hz performance of a control system subject to linear time-invariant uncertainties is considered. A set of upper bounds on the performance is derived, based on the theory of stability multipliers and the solution of an original optimal control problem. The numerical issues raised by the resulting computational problems are discussed, in particular, newly developed interior-point convex optimization methods, combined with linear matrix inequalities, apply very well to the fast and accurate solution of these problems. The new results compare favorably with prior ones. The method can ha extended to other types of perturbations.