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Mathematical Problems in Engineering
Volume 2012, Article ID 260236, 10 pages
Research Article

Semistability of Nonlinear Impulsive Systems with Delays

1Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
2College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Received 22 June 2012; Revised 23 August 2012; Accepted 15 September 2012

Academic Editor: Bo Shen

Copyright © 2012 Xiaowu Mu and Yongliang Gao. 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 stability analysis and semistability theorems for delay impulsive systems having a continuum of equilibria. We relate stability and semistability to the classical concepts of system storage functions to impulsive systems providing a generalized hybrid system energy interpretation in terms of storage energy. We show a set of Lyapunov-based sufficient conditions for establishing these stability properties. These make it possible to deduce properties of the Lyapunov functional and thus lead to sufficient conditions for stability and semistability. Our proposed results are evaluated using an illustrative example to show their effectiveness.