An overview of extremal properties for robust control of interval plants

Abstract

This paper provides an overview of recent results on the problem of robust stability and performance of feedback control systems in the presence of plant perturbations. The widely studied class of interval plants is considered, and an effort is made to cover different types of plant perturbations by incorporating, in addition to the interval plant description, unstructured norm bounded perturbations. Extremality results for these classes of uncertain systems are provided in a unifying framework. Robust performance of control systems is addressed in the paper and a number of extremal results are given for the computation of the structured singular value function for feedback systems with interval plants. Also, classical frequency response analysis for interval plant-controller families of open loop transfer functions is surveyed, with the aim of providing extremal results for the computation of specification parameters, such as phase or gain margins, and sensitivity and complementary sensitivity peaks.