Robust stability and performance of interval plants

In this paper we consider the problem of robust performance for 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 we show that in order to synthesize a controller that achieves 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 class of controllers with stronger results is also presented.