The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates
This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/639 |
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| author | WonIl Lee JaeWook Shin BumYong Park |
| author_facet | WonIl Lee JaeWook Shin BumYong Park |
| author_sort | WonIl Lee |
| collection | DOAJ |
| description | This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller. |
| first_indexed | 2024-04-25T00:24:33Z |
| format | Article |
| id | doaj.art-8be3032bc91a4953ab140dd0c42bc519 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:24:33Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8be3032bc91a4953ab140dd0c42bc5192024-03-12T16:49:47ZengMDPI AGMathematics2227-73902024-02-0112563910.3390/math12050639The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition RatesWonIl Lee0JaeWook Shin1BumYong Park2School of Electronic Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of KoreaSchool of Electronic Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of KoreaDepartment of IT Convergence Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of KoreaThis study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller.https://www.mdpi.com/2227-7390/12/5/639Markovian jump systemlinear matrix inequalitydissipativity control |
| spellingShingle | WonIl Lee JaeWook Shin BumYong Park The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates Mathematics Markovian jump system linear matrix inequality dissipativity control |
| title | The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates |
| title_full | The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates |
| title_fullStr | The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates |
| title_full_unstemmed | The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates |
| title_short | The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates |
| title_sort | strictly dissipative condition of continuous time markovian jump systems with uncertain transition rates |
| topic | Markovian jump system linear matrix inequality dissipativity control |
| url | https://www.mdpi.com/2227-7390/12/5/639 |
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