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

Jiang Wu (), Hao Xie (), Tianyi Li, Wenjian He, Tiancan Xi and Xiaoling Liang
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Jiang Wu: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Hao Xie: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Tianyi Li: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Wenjian He: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Tiancan Xi: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Xiaoling Liang: Maritime Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian 116026, China

Mathematics, 2025, vol. 13, issue 2, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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