On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems
The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/101485 |
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| _version_ | 1832564535648583680 |
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| author | Xinghua Liu Hongsheng Xi |
| author_facet | Xinghua Liu Hongsheng Xi |
| author_sort | Xinghua Liu |
| collection | DOAJ |
| description | The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov functional which contains some triple-integral terms is introduced. Then, by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability conditions are presented in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. |
| format | Article |
| id | doaj-art-5d0092666a284e4ead5a0119638a65f0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5d0092666a284e4ead5a0119638a65f02025-02-03T01:10:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/101485101485On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump SystemsXinghua Liu0Hongsheng Xi1Department of Automation, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaDepartment of Automation, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaThe delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov functional which contains some triple-integral terms is introduced. Then, by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability conditions are presented in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.http://dx.doi.org/10.1155/2013/101485 |
| spellingShingle | Xinghua Liu Hongsheng Xi On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems Journal of Applied Mathematics |
| title | On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems |
| title_full | On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems |
| title_fullStr | On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems |
| title_full_unstemmed | On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems |
| title_short | On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems |
| title_sort | on delay range dependent stochastic stability conditions of uncertain neutral delay markovian jump systems |
| url | http://dx.doi.org/10.1155/2013/101485 |
| work_keys_str_mv | AT xinghualiu ondelayrangedependentstochasticstabilityconditionsofuncertainneutraldelaymarkovianjumpsystems AT hongshengxi ondelayrangedependentstochasticstabilityconditionsofuncertainneutraldelaymarkovianjumpsystems |