Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback
This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/200 |
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| author | Jiang Wu Hao Xie Tianyi Li Wenjian He Tiancan Xi Xiaoling Liang |
| author_facet | Jiang Wu Hao Xie Tianyi Li Wenjian He Tiancan Xi Xiaoling Liang |
| author_sort | Jiang Wu |
| collection | DOAJ |
| description | This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-cda5ace77c4e4127a7267a481f16b9ef |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cda5ace77c4e4127a7267a481f16b9ef2025-01-24T13:39:43ZengMDPI AGMathematics2227-73902025-01-0113220010.3390/math13020200Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output FeedbackJiang Wu0Hao Xie1Tianyi Li2Wenjian He3Tiancan Xi4Xiaoling Liang5School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaMaritime Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian 116026, ChinaThis paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method.https://www.mdpi.com/2227-7390/13/2/200fractional-order systems with state time-delaysfinite-time bounded trackingoutput feedbacklinear matrix inequality |
| spellingShingle | Jiang Wu Hao Xie Tianyi Li Wenjian He Tiancan Xi Xiaoling Liang Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback Mathematics fractional-order systems with state time-delays finite-time bounded tracking output feedback linear matrix inequality |
| title | Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback |
| title_full | Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback |
| title_fullStr | Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback |
| title_full_unstemmed | Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback |
| title_short | Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback |
| title_sort | design of a finite time bounded tracking controller for time delay fractional order systems based on output feedback |
| topic | fractional-order systems with state time-delays finite-time bounded tracking output feedback linear matrix inequality |
| url | https://www.mdpi.com/2227-7390/13/2/200 |
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