Output Stabilization of Linear Systems in Given Set
This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the origi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3542 |
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| author | Ba Huy Nguyen Igor B. Furtat |
| author_facet | Ba Huy Nguyen Igor B. Furtat |
| author_sort | Ba Huy Nguyen |
| collection | DOAJ |
| description | This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the original system with output constraints into a new system without constraints. In the second stage, a controller is designed to ensure the boundedness of the controlled variable of the transformed system obtained in the first stage. Two distinct control strategies are presented in the second stage, depending on the measurability of the state vector. If the state vector is measurable, a controller is designed using state feedback based on the Lyapunov method and Linear Matrix Inequalities (LMIs). Alternatively, if only the output vector is measurable, an observer-based controller is designed using a Luenberger observer. In this case, the state estimation error does not need to converge to zero but must remain bounded. The efficacy of the proposed method and the validity of the theoretical results are demonstrated through simulations performed in MATLAB/Simulink. |
| first_indexed | 2024-03-10T23:45:21Z |
| format | Article |
| id | doaj.art-2e9aad9cd50a4580b68f5dfca9ba34fe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:21Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2e9aad9cd50a4580b68f5dfca9ba34fe2023-11-19T02:03:33ZengMDPI AGMathematics2227-73902023-08-011116354210.3390/math11163542Output Stabilization of Linear Systems in Given SetBa Huy Nguyen0Igor B. Furtat1Adaptive and Intelligent Control of Network and Distributed Systems Laboratory, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint-Petersburg, RussiaAdaptive and Intelligent Control of Network and Distributed Systems Laboratory, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint-Petersburg, RussiaThis paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the original system with output constraints into a new system without constraints. In the second stage, a controller is designed to ensure the boundedness of the controlled variable of the transformed system obtained in the first stage. Two distinct control strategies are presented in the second stage, depending on the measurability of the state vector. If the state vector is measurable, a controller is designed using state feedback based on the Lyapunov method and Linear Matrix Inequalities (LMIs). Alternatively, if only the output vector is measurable, an observer-based controller is designed using a Luenberger observer. In this case, the state estimation error does not need to converge to zero but must remain bounded. The efficacy of the proposed method and the validity of the theoretical results are demonstrated through simulations performed in MATLAB/Simulink.https://www.mdpi.com/2227-7390/11/16/3542linear dynamical systemchange of coordinatesstabilitycontrollinear matrix inequalities |
| spellingShingle | Ba Huy Nguyen Igor B. Furtat Output Stabilization of Linear Systems in Given Set Mathematics linear dynamical system change of coordinates stability control linear matrix inequalities |
| title | Output Stabilization of Linear Systems in Given Set |
| title_full | Output Stabilization of Linear Systems in Given Set |
| title_fullStr | Output Stabilization of Linear Systems in Given Set |
| title_full_unstemmed | Output Stabilization of Linear Systems in Given Set |
| title_short | Output Stabilization of Linear Systems in Given Set |
| title_sort | output stabilization of linear systems in given set |
| topic | linear dynamical system change of coordinates stability control linear matrix inequalities |
| url | https://www.mdpi.com/2227-7390/11/16/3542 |
| work_keys_str_mv | AT bahuynguyen outputstabilizationoflinearsystemsingivenset AT igorbfurtat outputstabilizationoflinearsystemsingivenset |