Robust control of feedback systems with combined plant and controller uncertainty

Consideration is given to the stability of feedback systems in the presence of combined plant and controller uncertainty. It is shown that if a controller C stabilizes a ball of plants about a nominal plant P, where distances are measured by the gap metric, then P stabilizes a ball of controllers about C of the same radius. This reveals a certain reciprocity between the roles of plant and controller in a feedback system. Necessary and sufficient conditions are given for plant stability under simultaneous perturbations of the plant and the controller. Also introduced is a weighted gap metric, and its application to the problem of robust stabilization of feedback systems is discussed.