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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/710741 |
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| _version_ | 1850170504486322176 |
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| author | Zixin Liu Jian Yu Daoyun Xu Dingtao Peng |
| author_facet | Zixin Liu Jian Yu Daoyun Xu Dingtao Peng |
| author_sort | Zixin Liu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9e253c03089a4000b80385aa3a7216fc |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9e253c03089a4000b80385aa3a7216fc2025-08-20T02:20:29ZengWileyJournal 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 |
| spellingShingle | Zixin Liu Jian Yu Daoyun Xu Dingtao Peng Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network Journal of Applied Mathematics |
| title | 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_short | Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network |
| title_sort | piecewise convex technique for the stability analysis of delayed neural network |
| 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 |