Abstract and Applied Analysis
Volume 2010 (2010), Article ID 987372, 11 pages
doi:10.1155/2010/987372
Research Article

Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

Shiguo Peng1 and Liping Yang2

1College of Automation, Guangdong University of Technology, Guangzhou 510006, China
2College of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Received 1 November 2009; Accepted 23 January 2010

Academic Editor: Yong Zhou

Copyright © 2010 Shiguo Peng and Liping Yang. 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 develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results.