Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays
The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals,...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/490515 |
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| _version_ | 1832566743969562624 |
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| author | Quanxin Zhu Jinde Cao |
| author_facet | Quanxin Zhu Jinde Cao |
| author_sort | Quanxin Zhu |
| collection | DOAJ |
| description | The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are
computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs.
A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI
criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given
in the previous literature. |
| format | Article |
| id | doaj-art-2cfba77474044361ad96e958d39f16b9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2cfba77474044361ad96e958d39f16b92025-02-03T01:03:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/490515490515Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed DelaysQuanxin Zhu0Jinde Cao1Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, Jiangsu, ChinaThe problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature.http://dx.doi.org/10.1155/2009/490515 |
| spellingShingle | Quanxin Zhu Jinde Cao Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays Discrete Dynamics in Nature and Society |
| title | Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays |
| title_full | Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays |
| title_fullStr | Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays |
| title_full_unstemmed | Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays |
| title_short | Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays |
| title_sort | stochastic stability of neural networks with both markovian jump parameters and continuously distributed delays |
| url | http://dx.doi.org/10.1155/2009/490515 |
| work_keys_str_mv | AT quanxinzhu stochasticstabilityofneuralnetworkswithbothmarkovianjumpparametersandcontinuouslydistributeddelays AT jindecao stochasticstabilityofneuralnetworkswithbothmarkovianjumpparametersandcontinuouslydistributeddelays |