Robust stability of general interconnections of interval plants and unstructured norm bounded perturbations

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.