Exponential stability of stochastic Hopfield neural network with mixed multiple delays

This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature...

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Published inAIMS mathematics Vol. 6; no. 4; pp. 4142 - 4155
Main Authors Zhou, Qinghua, Wan, Li, Fu, Hongbo, Zhang, Qunjiao
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
exponential stability
multiple time-varying delays
stochastic hopfield neural network
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Abstract This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.
AbstractList This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.
Author Zhou, Qinghua
Wan, Li
Fu, Hongbo
Zhang, Qunjiao
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Snippet This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and...
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SubjectTerms exponential stability
multiple time-varying delays
stochastic hopfield neural network
Title Exponential stability of stochastic Hopfield neural network with mixed multiple delays
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