Stability analysis by contraction principle for impulsive systems with infinite delays

Abstract

This paper studies a class of quasi-linear impulsive systems of functional differential equations with infinite time delay. By employing the contraction principle, several criteria on uniform stability and asymptotic stability are established. The proposed approach utilizes the idea of averaging instead of the point-wise estimate in the Lyapunov method. Our results show that the Banach contraction principle can be used as a possible alternative to Lyapunov methods for stability analysis when the conditions of Lyapunov method fails to hold. Several examples are discussed to illustrate the ideas of our results.