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Mathematics
Volume 13
Issue 2
10.3390/math13020200
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback

by
Jiang Wu
1,*,
Hao Xie
2,*,
Tianyi Li
2,
Wenjian He
2,
Tiancan Xi
2 and
Xiaoling Liang
3
1
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
3
Maritime Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian 116026, China
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(2), 200; https://doi.org/10.3390/math13020200
Submission received: 13 December 2024 / Revised: 6 January 2025 / Accepted: 8 January 2025 / Published: 9 January 2025
Versions Notes

Abstract

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.
Keywords: fractional-order systems with state time-delays; finite-time bounded tracking; output feedback; linear matrix inequality fractional-order systems with state time-delays; finite-time bounded tracking; output feedback; linear matrix inequality

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MDPI and ACS Style

Wu, J.; Xie, H.; Li, T.; He, W.; Xi, T.; Liang, X. Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback. Mathematics 2025, 13, 200. https://doi.org/10.3390/math13020200

AMA Style

Wu J, Xie H, Li T, He W, Xi T, Liang X. Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback. Mathematics. 2025; 13(2):200. https://doi.org/10.3390/math13020200

Chicago/Turabian Style

Wu, Jiang, Hao Xie, Tianyi Li, Wenjian He, Tiancan Xi, and Xiaoling Liang. 2025. "Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback" Mathematics 13, no. 2: 200. https://doi.org/10.3390/math13020200

APA Style

Wu, J., Xie, H., Li, T., He, W., Xi, T., & Liang, X. (2025). Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback. Mathematics, 13(2), 200. https://doi.org/10.3390/math13020200

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