On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/691650 |
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| _version_ | 1832554567913439232 |
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| author | Xinghua Liu Hongsheng Xi |
| author_facet | Xinghua Liu Hongsheng Xi |
| author_sort | Xinghua Liu |
| collection | DOAJ |
| description | The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods. |
| format | Article |
| id | doaj-art-5e394ec4bcef4a5fb1a3f3b234e1f295 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5e394ec4bcef4a5fb1a3f3b234e1f2952025-02-03T05:51:09ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/691650691650On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent DelaysXinghua Liu0Hongsheng Xi1Department of Auto, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaDepartment of Auto, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaThe exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.http://dx.doi.org/10.1155/2013/691650 |
| spellingShingle | Xinghua Liu Hongsheng Xi On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays Abstract and Applied Analysis |
| title | On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays |
| title_full | On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays |
| title_fullStr | On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays |
| title_full_unstemmed | On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays |
| title_short | On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays |
| title_sort | on exponential stability for a class of uncertain neutral markovian jump systems with mode dependent delays |
| url | http://dx.doi.org/10.1155/2013/691650 |
| work_keys_str_mv | AT xinghualiu onexponentialstabilityforaclassofuncertainneutralmarkovianjumpsystemswithmodedependentdelays AT hongshengxi onexponentialstabilityforaclassofuncertainneutralmarkovianjumpsystemswithmodedependentdelays |