Reduction model approach for linear time-varying systems with input delays based on extensions of Floquet theory |
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| Affiliation: | 1. EPI DISCO INRIA-Saclay, L2S, CNRS CentraleSupelec, 3 rue Joliot Curie, 91192 Gif-sur-Yvette, France;2. Department of Mathematics, 303 Lockett Hall, Louisiana State University, Baton Rouge, LA 70803-4918, USA;1. National Center for International Research on Structural Health Management of Critical Components, Jiangsu University, 301 Xuefu Road, Jingkou, Zhenjiang 212013, China;2. Faculty of Engineering, Tokyo University of Science, 6-3-1 Niijyuku, Katsushika-ku, Tokyo 1258585, Japan;3. Department of Aerospace Engineering, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates;1. Supercomputer Education and Research Center, Indian Institute of Science, Bangalore, India;2. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia;3. Novosibirsk State University, Novosibirsk, Russia;1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal;2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia;1. Birzeit University, Birzeit, Palestine;2. Department of Mathematics, University of Rijeka, Croatia |
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| Abstract: | We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We also prove an analogue for discrete time systems, through a discrete time extension of Floquet theory. |
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| Keywords: | Delay Time-varying Floquet theory Reduction model |
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