Exponential Stability of Neutral-Type Cohen-Grossberg Neural Networks With Multiple Time-Varying Delays

Li Wan,Qinghua Zhou

doi:10.1109/access.2021.3068191

Li Wan, Qinghua Zhou

Open Access

https://doi.org/10.1109/access.2021.3068191

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Abstract

This paper deals with the problem for exponential stability of a more general class of neutral-type Cohen-Grossberg neural networks. This class of neutral-type Cohen-Grossberg neural networks involves multiple time-varying delays in the states of neurons and multiple time-varying neutral delays in the time derivatives of the states of neurons. Such neural system cannot be described in the vector-matrix forms due to the existence of the multiple delays. The linear matrix inequality approach cannot be applied to this class of neutral system to determine the stability conditions. This paper provides some sufficient conditions to guarantee the existence, uniqueness and exponential stability of the equilibrium point of the neural system by employing the homeomorphism theory, Lyapunov-Krasovskii functional and inequality techniques. The provided conditions are easy to validate and can also guarantee the global asymptotic stability of the neural system. Two remarks are given to show the provided stability conditions are less conservative than the previous results. Two instructive examples are also given to demonstrate the effectiveness of the theoretical results and compare the provided stability conditions to the previous results.

Highlights

Since Cohen-Grossberg neural network was proposed [1], it has been extensively investigated by some mathematicians, physicists and computer scientists
There is a consensus that time delays always exists because the signal transmission between neurons usually has the phenomenon of limited transmission speed or traffic congestion
Time delay has a great influence on the neural network and it can make the stable network unstable or unstable network stable

Summary

Introduction

Since Cohen-Grossberg neural network was proposed [1], it has been extensively investigated by some mathematicians, physicists and computer scientists. As pointed out by [21] and [22], it is not possible to derive stability conditions of the linear matrix inequality forms for the neutral-type neural networks that cannot be expressed in the vector-matrix form. Zhou: Exponential Stability of Neutral-Type Cohen-Grossberg Neural Networks conditions.

Results

Conclusion