Robust Control of Feedback Systems with Combined Plant and Controller Uncertainty

In this paper we consider the stability of feedback systems in the presence of combined plant and controller uncertainty. We show 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 role of plant and controller in a feedback system. We give a necessary and sufficient condition for stability under simultaneous perturbations of the plant and the controller. We also introduce a weighted gap metric and discuss its application to the problem of robust stabilization of feedback systems.