2022-10-01T17:01:22Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000120452021-03-01T19:03:22ZA Floquet-like factorization for linear periodic systemsJikuya, Ichiro38197Hodaka, Ichijo38198In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the well-known Floquet representation theorem, a 2T-periodic real-valued factor and a real-valued matrix exponential function are extracted from the state transition matrix. Then we also proved that any T-periodic system can be transformed to a system with T-periodic real-valued trigonometric coefficients using a T-periodic real-valued coordinate transformation, while, in the well-known Lyapunov reducibility theorem, a 2T-periodic real-valued coordinate transformation is utilized to transform the given periodic system into a time-invariant system with real coefficients. This new information can be useful for designing a T-periodic control law.journal articleIEEE2009-12-15application/pdfProceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference (CDC/CCC 2009)64326437http://hdl.handle.net/2237/13921http://dx.doi.org/10.1109/CDC.2009.54008930191-2216https://nagoya.repo.nii.ac.jp/record/12045/files/jikuya.pdfeng©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.