Fixed-time stabilization of periodic linear systems and its application to the elliptical spacecraft rendezvous |
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| Institution: | 1. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China;1. School of Cyber Science and Engineering, Sichuan University, Chengdu 610065, China;2. School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China;3. School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China;4. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610050, China;1. College of Automation & Information Engineering, and Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan University of Science & Engineering, Zigong 643000, China;2. College of Engineering, Huazhong Agricultural University, Wuhan 430070, China;3. School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, SA 5005, Australia;1. School of Automation,Central South University,Changsha,410083, China;2. Department of Electrical and Electronic Engineering, Chiba University, Chiba,263–8522,Japan;1. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;2. School of Automation, Southeast University, Nanjing, Jiangsu, 210096, China |
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| Abstract: | 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. |
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