Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates
The problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/950590 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559214340341760 |
|---|---|
| author | Mengzhuo Luo Shouming Zhong |
| author_facet | Mengzhuo Luo Shouming Zhong |
| author_sort | Mengzhuo Luo |
| collection | DOAJ |
| description | The problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov-Krasovskii functional (LKF) combining with Jensen’s inequality and the free-weighting matrix method, delay-dependent exponential passification conditions are obtained in terms of linear matrix inequalities (LMI). Based on the condition, desired state-feedback controllers are designed, which guarantee that the closed-loop MJS is exponentially passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach. |
| format | Article |
| id | doaj-art-6afbbf51c6cd4e93b9cb3375d0e327b3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6afbbf51c6cd4e93b9cb3375d0e327b32025-02-03T01:30:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/950590950590Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition RatesMengzhuo Luo0Shouming Zhong1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaThe problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov-Krasovskii functional (LKF) combining with Jensen’s inequality and the free-weighting matrix method, delay-dependent exponential passification conditions are obtained in terms of linear matrix inequalities (LMI). Based on the condition, desired state-feedback controllers are designed, which guarantee that the closed-loop MJS is exponentially passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.http://dx.doi.org/10.1155/2012/950590 |
| spellingShingle | Mengzhuo Luo Shouming Zhong Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates Journal of Applied Mathematics |
| title | Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates |
| title_full | Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates |
| title_fullStr | Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates |
| title_full_unstemmed | Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates |
| title_short | Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates |
| title_sort | exponential passification of markovian jump nonlinear systems with partially known transition rates |
| url | http://dx.doi.org/10.1155/2012/950590 |
| work_keys_str_mv | AT mengzhuoluo exponentialpassificationofmarkovianjumpnonlinearsystemswithpartiallyknowntransitionrates AT shoumingzhong exponentialpassificationofmarkovianjumpnonlinearsystemswithpartiallyknowntransitionrates |