Abstract and Applied Analysis
Volume 2013 (2013), Article ID 938027, 6 pages
http://dx.doi.org/10.1155/2013/938027
Research Article

Exponential Stability of Impulsive Delay Differential Equations

G. L. Zhang, M. H. Song, and M. Z. Liu

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 8 September 2012; Revised 3 January 2013; Accepted 8 January 2013

Academic Editor: Xinan Hao

Copyright © 2013 G. L. Zhang et al. 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

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.