Metric uncertainty and nonlinear feedback stabilization

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.