Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty

Abstract

With the development of intelligent control, switched systems have been widely studied. Here we try to introduce some ideas of the switched systems into the field of neural networks. In this Letter, a class of switched Hopfield neural networks with time-varying delay is investigated. The parametric uncertainty is considered and assumed to be norm bounded. Firstly, the mathematical model of the switched Hopfield neural networks is established in which a set of Hopfield neural networks are used as the individual subsystems and an arbitrary switching rule is assumed; Secondly, robust stability analysis for such switched Hopfield neural networks is addressed based on the Lyapunov–Krasovskii approach. Some criteria are given to guarantee the switched Hopfield neural networks to be globally exponentially stable for all admissible parametric uncertainties. These conditions are expressed in terms of some strict linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate our results.