In this paper, we consider robust controller design problems where the design objectives are divided into two categories: hard specifications and soft specifications. Hard specifications need to be met robustly against uncertainties, and are addressed using a classical H-infinity/mu-synthesis approach. Soft specifications are given as average performance requirements with respect to uncertainty, and are addressed using a probabilistic design method. The key element in this approach is an algorithm for random generation of stable transfer matrices, with a bound on the H-infinity norm.