Metric Uncertainty and Nonlinear Feedback Stabilization

T.T. Georgiou and M.C. Smith

Abstract

In this paper we define a generalization of the gap metric for nonlinear systems. We prove two results which specialize to known results for linear systems. First, we show that a feedback system remains stable if the distance between the plant and its perturbation is less than the inverse of the norm of a certain parallel projection operator. Second, we show that every ``continuously robust'' metric on nonlinear systems is equivalent to the metric introduced in this paper.