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Mathematical Problems in Engineering
Volume 2013, Article ID 458047, 7 pages
Research Article

The Method of Lyapunov Function and Exponential Stability of Impulsive Delay Systems with Delayed Impulses

1School of Mathematical Sciences, Anhui University, Hefei 230601, China
2Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China

Received 4 September 2013; Revised 5 November 2013; Accepted 5 November 2013

Academic Editor: Bo Shen

Copyright © 2013 Pei Cheng 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.


This paper investigates the exponential stability of general impulsive delay systems with delayed impulses. By using the Lyapunov function method, some Lyapunov-based sufficient conditions for exponential stability are derived, which are more convenient to be applied than those Razumikhin-type conditions in the literature. Their applications to linear impulsive systems with time-varying delays are also proposed, and a set of sufficient conditions for exponential stability is provided in terms of matrix inequalities. Meanwhile, two examples are discussed to illustrate the effectiveness and advantages of the results obtained.