Fixed-time stabilization of periodic linear systems and its application to the elliptical spacecraft rendezvous

A smooth periodic delayed feedback (SPDF) control scheme is proposed for the fixed-time stabilization problem of linear periodic systems subject to input delay. By investigating the monodromy matrix of the periodic system, it is proved that the SPDF controller can achieve the fixed-time stabilizatio...

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Bibliographic Details
Published inJournal of the Franklin Institute Vol. 360; no. 12; pp. 7832 - 7850
Main Authors Zhang, Zhe, Jiang, Huaiyuan, Yang, Xuefei
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2023
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ISSN0016-0032
1879-2693
DOI10.1016/j.jfranklin.2023.06.020

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Summary:A smooth periodic delayed feedback (SPDF) control scheme is proposed for the fixed-time stabilization problem of linear periodic systems subject to input delay. By investigating the monodromy matrix of the periodic system, it is proved that the SPDF controller can achieve the fixed-time stabilization of linear periodic systems with arbitrarily long yet bounded input delays under the condition that the original system is uniformly completely controllable. The proposed controller is continuously differentiable and smooth. The SPDF control scheme is then applied to the elliptical spacecraft rendezvous problem. The effectiveness of the established method is verified on numerical simulations.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2023.06.020