Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order...

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Published inIEEE transaction on neural networks and learning systems Vol. 34; no. 10; pp. 7491 - 7499
Main Authors Lin, Hui-Chao, Zeng, Hong-Bing, Zhang, Xian-Ming, Wang, Wei
Format Journal Article
LanguageEnglish
Published United States IEEE 01.10.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Artificial neural networks
Delayed neural network (NN)
Delays
Linear matrix inequalities
Lyapunov-Krasovskii functional (LKF)
Neural networks
Neurons
reciprocally convex combination
Stability analysis
Stability criteria
Symmetric matrices
Time-varying systems
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Abstract This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.
AbstractList This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.
This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.
Author Lin, Hui-Chao
Wang, Wei
Zhang, Xian-Ming
Zeng, Hong-Bing
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Snippet This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented,...
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SubjectTerms Artificial neural networks
Delayed neural network (NN)
Delays
Linear matrix inequalities
Lyapunov-Krasovskii functional (LKF)
Neural networks
Neurons
reciprocally convex combination
Stability analysis
Stability criteria
Symmetric matrices
Time-varying systems
Title Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality
URI https://ieeexplore.ieee.org/document/9701669
https://www.ncbi.nlm.nih.gov/pubmed/35108209
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Volume 34
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