Advances in Difference Equations
Volume 2010 (2010), Article ID 726347, 15 pages
Research Article

A Converse Lyapunov Theorem and Robustness with Respect to Unbounded Perturbations for Exponential Dissipativity

Department of Mathematics, Lanzhou City University, Lanzhou 730070, China

Received 18 December 2009; Revised 19 March 2010; Accepted 17 April 2010

Academic Editor: Josef Diblik

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.


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.