Extremal properties for the parametric robust performance problem

The authors consider the problem of robust performance of systems with unstructured and parametric perturbations. The parametric uncertainty is modeled through a single-input-single-output interval system description, and the unstructured uncertainty through a norm-bounded perturbation. For this type of parametric robust performance, it is shown that to synthesize a controller that will achieve robust performance for a family of interval systems, it is sufficient to synthesize that controller for a much smaller subset of the interval family. Regardless of the number of uncertain parameters in the original problem, this reduced set is composed of thirty two one-parameter families of systems. A special case with stronger results is also presented