Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems†
1
School of Information Engineering, Xiangtan University, Xiangtan 411105, China
2
Led Lighting Research And Technology Center of Guizhou, Tongren 554300, China.
*
Author to whom correspondence should be addressed.
†
This work was supported in part by the National Natural Science Foundation of China (61573298) and the Scientific Research Fund of Hunan Provincial Education Department (15B238).
Algorithms 2019, 12(1), 20; https://doi.org/10.3390/a12010020
Received: 14 November 2018 / Revised: 4 January 2019 / Accepted: 4 January 2019 / Published: 10 January 2019
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.
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MDPI and ACS Style
Lan, Y.-H.; Xia, J.-J.; Shi, Y.-X. Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems. Algorithms 2019, 12, 20. https://doi.org/10.3390/a12010020
AMA Style
Lan Y-H, Xia J-J, Shi Y-X. Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems. Algorithms. 2019; 12(1):20. https://doi.org/10.3390/a12010020
Chicago/Turabian StyleLan, Yong-Hong; Xia, Jun-Jun; Shi, Yue-Xiang. 2019. "Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems" Algorithms 12, no. 1: 20. https://doi.org/10.3390/a12010020
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