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Open AccessArticle

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. View Full-Text
Keywords: robust control; preview control; repetitive control; controller design; uncertain systems robust control; preview control; repetitive control; controller design; uncertain systems
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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 Style

Lan, 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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