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The Scientific World Journal
Volume 2014, Article ID 932395, 8 pages
http://dx.doi.org/10.1155/2014/932395
Research Article

Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

1School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, China
2Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria

Received 1 August 2013; Accepted 2 December 2013; Published 27 February 2014

Academic Editors: A. Favini and O. Kwon

Copyright © 2014 Xuling Wang 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

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.