Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

Zhang, Qianhong; Shao, Yuanfu; Liu, Jingzhong

doi:10.1002/mma.2624

Cited by 15 publications

(7 citation statements)

References 29 publications

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“…Fundamental theory of impulsive differential equations has been developed in [7]. Furthermore, researches of impulsive differential equations have been received much interesting in recent years [8][9][10][11][12][13][14][15][16][17][18]. Meanwhile, several kinds of neural networks with impulse have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

Chiu

2013

Abstract and Applied Analysis

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We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach's fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

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Section: Introductionmentioning

confidence: 99%

Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

Chiu

2013

Abstract and Applied Analysis

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“…In this section, we shall establish the simple stability criterion for Hopfield neural networks to illustrate the effectiveness of our theoretical results. Some stability results for neural networks with time delay and fixed impulses could be found in [34][35][36][37][38]. Consider the following system 8 <…”

Section: Application To Neural Networkmentioning

confidence: 99%

Stability criteria in terms of two measures for functional differential equation with variable‐time impulses

Liu

Huang

et al. 2014

Math Methods in App Sciences

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This paper focuses on the stability in terms of two measures for functional differential equation with variable‐time impulses. Being different from most of existing literatures, the impulses of functional differential equation are assumed to be closely associated to the current state. We propose a new comparison principle for the considered systems and establish several stability criteria in terms of two measures. Also, the theoretical results are applied in a class of delayed neural network systems with variable‐tine impulses, and numerical simulations are introduced to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.

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“…It is a very useful tool in image processing and pattern recognition. However, the existence of time delays may lead to the instability or bad performance of systems [5][6][7]. So, it is of prime importance to consider the delay effects on the dynamical behavior of systems.…”

Section: Introductionmentioning

confidence: 99%

Asymptotical state estimation of fuzzy cellular neural networks with time delay in the leakage term and mixed delays: Sample-data approach

Kalpana

Balasubramaniam

2016

Journal of the Egyptian Mathematical Society

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In this paper, the sampled measurement is used to estimate the neuron states, instead of the continuous measurement, and a sampled-data estimator is constructed. Leakage delay is used to unstable the neuron states. It is a challenging task to develop delay dependent condition to estimate the unstable neuron states through available sampled output measurements such that the error-state system is globally asymptotically stable. By constructing Lyapunov-Krasovskii functional (LKF), a sufficient condition depending on the sampling period is obtained in terms of linear matrix inequalities (LMIs). Moreover, by using the free-weighting matrices method, simple and efficient criterion is derived in terms of LMIs for estimation. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 03B52; 92B20; 93C57; 93D20 ª 2015 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.

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Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

Cited by 15 publications

References 29 publications

Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

Stability criteria in terms of two measures for functional differential equation with variable‐time impulses

Asymptotical state estimation of fuzzy cellular neural networks with time delay in the leakage term and mixed delays: Sample-data approach

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