New Results of Global Asymptotical Stability for Impulsive Hopfield Neural Networks with Leakage Time-Varying Delay

Qiang Xi

doi:10.4236/jamp.2017.511173

Abstract

In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).

Highlights

As we know, time delay is a common phenomenon that describes the fact that the future state of a system depends on the present state and on the past state, and often encountered in many fields such as automatic control, biological chemistry, physical engineer, neural networks, and so on [1] [2] [3] [4] [5]
New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques
The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI)

Summary

Introduction

Time delay is a common phenomenon that describes the fact that the future state of a system depends on the present state and on the past state, and often encountered in many fields such as automatic control, biological chemistry, physical engineer, neural networks, and so on [1] [2] [3] [4] [5]. In [27], Gopalsamy initially investigated the dynamics of bidirectional associative memory (BAM) network model with leakage delays by using model transformation technique, Lyapunov-Kravsovskii functional and inequalities together with some properties of M-matrices. Li et al [35], initially studies the impulsive effects on existence-uniqueness and stability problems of recurrent neural networks with leakage delay via some analysis techniques on impulsive functional differential equations. Stability research on leakage time-varying delay has been hardly considered in the literature. It is interesting to consider neural networks with leakage time-varying delay as well as impulse, which describes more realistic models [37]-[40]. In this paper, we consider Hopfield neural networks with leakage time-varying delay and impulse.

Preliminaries

Global Asymptotic Stability

Conclusion