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.

Abstract

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.