Asymptotic behavior of nonlinear systems with impulses: Application to Hopfield neural networks

Abstract

In this paper, we provide some sufficient conditions for the exponential stability of solutions of nonlinear impulsive differential systems by using some inequality of Gronwall-Bellman type. Practical exponential stability is also investigated for a class of perturbed impulsive systems. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results. Furthermore, Hopfield neural networks system is discussed as an application.