Randomization in ℛH∞: an approach to control 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 uncertainties, and axe addressed using a classical H_∞μ-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_∞ norm.