Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System
This paper addresses the robust finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to sho...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9567705/ |
| _version_ | 1818742315500437504 |
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| author | Yang Ding Hang Zhang Tianbo Wang |
| author_facet | Yang Ding Hang Zhang Tianbo Wang |
| author_sort | Yang Ding |
| collection | DOAJ |
| description | This paper addresses the robust finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to show that the singular system is finite-time stability by using the state space decomposition approach. Similar with the proof method of this Lemma, the singular system is divided into a differential system and an algebra one. Then, some conditions are derived to ensure the singular system being finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stability based on the obtained lemma, and the state feedback control law is designed. These conditions are provided in the form of the linear matrix inequalities and can be easily solved. Finally, a numerical example is given to illustrate the effectiveness of the obtained results. |
| first_indexed | 2024-12-18T02:10:34Z |
| format | Article |
| id | doaj.art-8f0011c288f94759b165617cd60f4aeb |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-18T02:10:34Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8f0011c288f94759b165617cd60f4aeb2022-12-21T21:24:29ZengIEEEIEEE Access2169-35362021-01-01913950813951510.1109/ACCESS.2021.31194089567705Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular SystemYang Ding0https://orcid.org/0000-0002-1056-688XHang Zhang1https://orcid.org/0000-0001-8056-8138Tianbo Wang2https://orcid.org/0000-0003-0765-1693School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, ChinaThis paper addresses the robust finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to show that the singular system is finite-time stability by using the state space decomposition approach. Similar with the proof method of this Lemma, the singular system is divided into a differential system and an algebra one. Then, some conditions are derived to ensure the singular system being finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stability based on the obtained lemma, and the state feedback control law is designed. These conditions are provided in the form of the linear matrix inequalities and can be easily solved. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.https://ieeexplore.ieee.org/document/9567705/Finite-time stability<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ controlsingular systemuncertainty |
| spellingShingle | Yang Ding Hang Zhang Tianbo Wang Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System IEEE Access Finite-time stability <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ control singular system uncertainty |
| title | Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System |
| title_full | Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System |
| title_fullStr | Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System |
| title_full_unstemmed | Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System |
| title_short | Robust Finite-Time <italic>H</italic>∞ Control for the Uncertain Singular System |
| title_sort | robust finite time italic h italic x221e control for the uncertain singular system |
| topic | Finite-time stability <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ control singular system uncertainty |
| url | https://ieeexplore.ieee.org/document/9567705/ |
| work_keys_str_mv | AT yangding robustfinitetimeitalichitalicx221econtrolfortheuncertainsingularsystem AT hangzhang robustfinitetimeitalichitalicx221econtrolfortheuncertainsingularsystem AT tianbowang robustfinitetimeitalichitalicx221econtrolfortheuncertainsingularsystem |