Truncated predictor feedback for linear systems with long time-varying input delays |
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| Authors: | Bin Zhou Zongli Lin Guang-Ren Duan |
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| Affiliation: | 1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;2. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743-4743, Charlottesville, VA 22904-4743, USA;1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China;2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;3. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743-4743, Charlottesville, VA 22904-4743, USA;1. LUNAM Université, Ecole Centrale de Nantes, IRCCyN UMR CNRS 6597, Nantes, France;2. Xlim-SIC, Université de Poitiers, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France;1. State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, PR China;2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA |
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| Abstract: | In this paper we study the problem of stabilizing a linear system with a single long time-varying delay in the input. Under the assumption that the open-loop system is stabilizable and not exponentially unstable, a finite dimensional static time-varying linear state feedback controller is obtained by truncating the predictor based controller and by adopting the parametric Lyapunov equation based controller design approach. As long as the time-varying delay is exactly known and bounded, an explicit condition is provided to guarantee the stability of the closed-loop system. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints. Numerical examples show the effectiveness of the proposed approach. |
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