Finite-Time Control of Singular Linear Semi-Markov Jump Systems
The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular line...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/1/8 |
| _version_ | 1827667170253864960 |
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| author | Xiaofu Ji Xuehua Liu |
| author_facet | Xiaofu Ji Xuehua Liu |
| author_sort | Xiaofu Ji |
| collection | DOAJ |
| description | The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method. |
| first_indexed | 2024-03-10T03:04:58Z |
| format | Article |
| id | doaj.art-b39f42ecf7f344469251be69ea761113 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T03:04:58Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-b39f42ecf7f344469251be69ea7611132023-11-23T12:40:31ZengMDPI AGAlgorithms1999-48932021-12-01151810.3390/a15010008Finite-Time Control of Singular Linear Semi-Markov Jump SystemsXiaofu Ji0Xuehua Liu1Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry, Ministry of Education, School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, ChinaThe problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.https://www.mdpi.com/1999-4893/15/1/8singular linear systemSMJSstochastic finite-time stabilizationlinear matrix inequality |
| spellingShingle | Xiaofu Ji Xuehua Liu Finite-Time Control of Singular Linear Semi-Markov Jump Systems Algorithms singular linear system SMJS stochastic finite-time stabilization linear matrix inequality |
| title | Finite-Time Control of Singular Linear Semi-Markov Jump Systems |
| title_full | Finite-Time Control of Singular Linear Semi-Markov Jump Systems |
| title_fullStr | Finite-Time Control of Singular Linear Semi-Markov Jump Systems |
| title_full_unstemmed | Finite-Time Control of Singular Linear Semi-Markov Jump Systems |
| title_short | Finite-Time Control of Singular Linear Semi-Markov Jump Systems |
| title_sort | finite time control of singular linear semi markov jump systems |
| topic | singular linear system SMJS stochastic finite-time stabilization linear matrix inequality |
| url | https://www.mdpi.com/1999-4893/15/1/8 |
| work_keys_str_mv | AT xiaofuji finitetimecontrolofsingularlinearsemimarkovjumpsystems AT xuehualiu finitetimecontrolofsingularlinearsemimarkovjumpsystems |