Copyright © 2010 Xudong Li and Yuan Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the nonlinear system x′(t)=f(t,x(t)). We give a converse Lyapunov theorem and prove robustness of uniform exponential dissipativity with respect to unbounded external perturbations, without assuming f being globally Lipschitz in x.