Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump
This paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely un...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9450786 |
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| _version_ | 1832552070124666880 |
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| author | Yanbo Li Chao-Yang Chen Chengqun Li |
| author_facet | Yanbo Li Chao-Yang Chen Chengqun Li |
| author_sort | Yanbo Li |
| collection | DOAJ |
| description | This paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely unknown. Based on calculating the weak infinitesimal generator and combining Poincare inequality and Green formula, a stochastic stability criterion is given in terms of a set of linear matrix inequalities (LMIs) by the Schur complement lemma. Because of the existence of the neutral term, we need to construct Lyapunov functionals showing more complexity to handle the cross terms involving the Laplace operator. Finally, a numerical example is provided to support the validity of the mathematical results. |
| format | Article |
| id | doaj-art-2d8831e5ea0c42138bb9e64f8e52df0f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2d8831e5ea0c42138bb9e64f8e52df0f2025-02-03T05:59:35ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/94507869450786Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian JumpYanbo Li0Chao-Yang Chen1Chengqun Li2School of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530001, ChinaSchool of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, ChinaSchool of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530001, ChinaThis paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely unknown. Based on calculating the weak infinitesimal generator and combining Poincare inequality and Green formula, a stochastic stability criterion is given in terms of a set of linear matrix inequalities (LMIs) by the Schur complement lemma. Because of the existence of the neutral term, we need to construct Lyapunov functionals showing more complexity to handle the cross terms involving the Laplace operator. Finally, a numerical example is provided to support the validity of the mathematical results.http://dx.doi.org/10.1155/2020/9450786 |
| spellingShingle | Yanbo Li Chao-Yang Chen Chengqun Li Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump Complexity |
| title | Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump |
| title_full | Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump |
| title_fullStr | Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump |
| title_full_unstemmed | Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump |
| title_short | Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump |
| title_sort | stochastic stability criteria for neutral distributed parameter systems with markovian jump |
| url | http://dx.doi.org/10.1155/2020/9450786 |
| work_keys_str_mv | AT yanboli stochasticstabilitycriteriaforneutraldistributedparametersystemswithmarkovianjump AT chaoyangchen stochasticstabilitycriteriaforneutraldistributedparametersystemswithmarkovianjump AT chengqunli stochasticstabilitycriteriaforneutraldistributedparametersystemswithmarkovianjump |