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タイトル: Delayed Feedback Control by Commutative Gain Matrices
著者: Miyazaki, Rinko
Naito, Toshiki
Shin, Jong Son
掲載誌名: SIAM Journal on Mathematical Analysis
出版者: Society for Industrial and Applied Mathematics
巻: 43
号: 3
開始ページ: 1122
終了ページ: 1144
出版日付: 2011-05-05
権利: © 2011 Society for Industrial and Applied Mathematics
NDC: 413
抄録: The delayed feedback control (DFC) is a control method for stabilizing unstable periodic orbits in nonlinear autonomous differential equations. We give an important relationship between the characteristic multipliers of the linear variational equation around an unstable periodic solution of the equation and those of its delayed feedback equation. The key of our proof is a result about the spectrum of a matrix which is a difference of commutative matrices. The relationship, moreover, allows us to design control gains of the DFC such that the unstable periodic solution is stabilized. In other words, the validity of the DFC is proved mathematically. As an application for the Rössler equation, we determine the best range of $k$ such that the unstable periodic orbit is stabilized by taking a feedback gain $K=kE$.
ISSN: 00361410 OPAC
出版者DOI: 10.1137/090779450   
NII書誌ID: AA00424217 OPAC ciniib
バージョン: publisher
出現コレクション:05. 雑誌論文・記事(Journal Article, Article, Preprint)

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Others By: Miyazaki, Rinko (宮崎, 倫子) (ミヤザキ, リンコ) -- Naito, Toshiki -- Shin, Jong Son



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