Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive...

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Main Authors: Zixin Liu, Jian Yu, Daoyun Xu, Dingtao Peng
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/710741
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spelling doaj-9e253c03089a4000b80385aa3a7216fc2020-11-24T22:38:35ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/710741710741Piecewise Convex Technique for the Stability Analysis of Delayed Neural NetworkZixin Liu0Jian Yu1Daoyun Xu2Dingtao Peng3College of Computer Science and Information, Guizhou University, Guiyang 550025, ChinaCollege of Computer Science and Information, Guizhou University, Guiyang 550025, ChinaCollege of Computer Science and Information, Guizhou University, Guiyang 550025, ChinaCollege of Science, Guizhou University, Guiyang 550025, ChinaOn the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results.http://dx.doi.org/10.1155/2013/710741
collection DOAJ
language English
format Article
sources DOAJ
author Zixin Liu
Jian Yu
Daoyun Xu
Dingtao Peng
spellingShingle Zixin Liu
Jian Yu
Daoyun Xu
Dingtao Peng
Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
Journal of Applied Mathematics
author_facet Zixin Liu
Jian Yu
Daoyun Xu
Dingtao Peng
author_sort Zixin Liu
title Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
title_short Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
title_full Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
title_fullStr Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
title_full_unstemmed Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network
title_sort piecewise convex technique for the stability analysis of delayed neural network
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results.
url http://dx.doi.org/10.1155/2013/710741
work_keys_str_mv AT zixinliu piecewiseconvextechniqueforthestabilityanalysisofdelayedneuralnetwork
AT jianyu piecewiseconvextechniqueforthestabilityanalysisofdelayedneuralnetwork
AT daoyunxu piecewiseconvextechniqueforthestabilityanalysisofdelayedneuralnetwork
AT dingtaopeng piecewiseconvextechniqueforthestabilityanalysisofdelayedneuralnetwork
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