Randomization in RH∞: An approach to controller design with hard/soft performance specifications

In this paper, we consider a robust controller design problem, where the design objectives are divided into two categories: Hard specifications and soft specifications. Hard specifications need to be met robustly against un-certainties, and are addressed using a classical H∞/µ-synthesis approach. Soft specifications are given as average performance requirements with re-spect 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 ∞ norm.