Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay
The problems of stochastic stability and stabilization for a class of Markovian jump distributed parameter systems with time delay are researched in this paper. First, taking advantage of a combination of Poincare inequality and Green formula, a stochastic stability criterion is presented by a linea...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8765308/ |
| _version_ | 1818603723128045568 |
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| author | Yanbo Li Chaoyang Chen Baoxian Wang |
| author_facet | Yanbo Li Chaoyang Chen Baoxian Wang |
| author_sort | Yanbo Li |
| collection | DOAJ |
| description | The problems of stochastic stability and stabilization for a class of Markovian jump distributed parameter systems with time delay are researched in this paper. First, taking advantage of a combination of Poincare inequality and Green formula, a stochastic stability criterion is presented by a linear matrix inequality (LMI) approach. Then, a state feedback controller is designed. Based on the proposed results, the sufficient conditions of the close-loop systems' stochastic stability are given in terms of a set of LMIs by constructing the appropriate Lyapunov functionals, calculating the weak infinitesimal generator, and using the Schur complement lemma. The sufficient conditions could be solved directly and applied to engineering practice conveniently. The obtained results generalize and enrich the theory of distributed parameter systems with time delay. The model of Markovian jump distributed parameter systems is more fitting the actual systems' requirements and has wider application scope. Finally, numerical examples are used to demonstrate the validity of the method. |
| first_indexed | 2024-12-16T13:27:42Z |
| format | Article |
| id | doaj.art-db63d47772924af98d380e88972bc736 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T13:27:42Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-db63d47772924af98d380e88972bc7362022-12-21T22:30:10ZengIEEEIEEE Access2169-35362019-01-01710393110393710.1109/ACCESS.2019.29294948765308Stabilization for Markovian Jump Distributed Parameter Systems With Time DelayYanbo Li0Chaoyang Chen1https://orcid.org/0000-0002-8095-399XBaoxian Wang2School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, ChinaSchool of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, ChinaCollege of Science, China Three Gorges University, Yichang, ChinaThe problems of stochastic stability and stabilization for a class of Markovian jump distributed parameter systems with time delay are researched in this paper. First, taking advantage of a combination of Poincare inequality and Green formula, a stochastic stability criterion is presented by a linear matrix inequality (LMI) approach. Then, a state feedback controller is designed. Based on the proposed results, the sufficient conditions of the close-loop systems' stochastic stability are given in terms of a set of LMIs by constructing the appropriate Lyapunov functionals, calculating the weak infinitesimal generator, and using the Schur complement lemma. The sufficient conditions could be solved directly and applied to engineering practice conveniently. The obtained results generalize and enrich the theory of distributed parameter systems with time delay. The model of Markovian jump distributed parameter systems is more fitting the actual systems' requirements and has wider application scope. Finally, numerical examples are used to demonstrate the validity of the method.https://ieeexplore.ieee.org/document/8765308/Markovian jumpdistributed parameter systemsstochastic stabilitylinear matrix inequality |
| spellingShingle | Yanbo Li Chaoyang Chen Baoxian Wang Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay IEEE Access Markovian jump distributed parameter systems stochastic stability linear matrix inequality |
| title | Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay |
| title_full | Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay |
| title_fullStr | Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay |
| title_full_unstemmed | Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay |
| title_short | Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay |
| title_sort | stabilization for markovian jump distributed parameter systems with time delay |
| topic | Markovian jump distributed parameter systems stochastic stability linear matrix inequality |
| url | https://ieeexplore.ieee.org/document/8765308/ |
| work_keys_str_mv | AT yanboli stabilizationformarkovianjumpdistributedparametersystemswithtimedelay AT chaoyangchen stabilizationformarkovianjumpdistributedparametersystemswithtimedelay AT baoxianwang stabilizationformarkovianjumpdistributedparametersystemswithtimedelay |