Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations

Abstract

This paper introduces a new class of functions called inverse Lipschitz functions ( I L ). By using I L , a novel class of neural networks with inverse Lipschitz neuron activation functions is presented. By the topological degree theory and matrix inequality techniques, the existence and uniqueness of equilibrium point for the neural network are investigated. By constructing appropriate Lyapunov functions, a sufficient condition ensuring global exponential stability of the neural network is given. At last, two numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.