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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kalman–Yakubovich–Popov lemma ： ウィキペディア英語版 Kalman–Yakubovich–Popov lemma The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number $\backslash gamma\; >\; 0$, two n-vectors B, C and an n x n Hurwitz matrix A, if the pair $(A,B)$ is completely controllable, then a symmetric matrix P and a vector Q satisfying :$A^T\; P\; +\; P\; A\; =\; -Q\; Q^T\backslash ,$ :$P\; B-C\; =\; \backslash sqrtQ\backslash ,$ exist if and only if :$$ \gamma+2 Re((j\omega I-A)^B )\ge 0 Moreover, the set $\backslash$ is the unobservable subspace for the pair $(A,B)$. The lemma can be seen as a generalization of the Lyapunov equation in stability theory. It establishes a relation between a linear matrix inequality involving the state space constructs A, B, C and a condition in the frequency domain. It was derived in 1962 by Rudolf E. Kalman, who brought together results by Vladimir Andreevich Yakubovich and Vasile Mihai Popov. ==Multivariable Kalman–Yakubovich–Popov lemma== Given $A\; \backslash in\; \backslash R^,\; B\; \backslash in\; \backslash R^,\; M\; =\; M^T\; \backslash in\; \backslash R^$ with $\backslash det(j\backslash omega\; I\; -\; A)\; \backslash ne\; 0$ for all $\backslash omega\; \backslash in\; \backslash R$ and $(A,\; B)$ controllable, the following are equivalent: for all $\backslash omega\; \backslash in\; \backslash R\; \backslash cup\; \backslash$ :$\backslash left((j\backslash omega\; I\; -\; A)^B\; \backslash \backslash \; I\; \backslash end\backslash right)^$ * M \left((j\omega I - A)^B \\ I \end\right ) \le 0 there exists a matrix $P\; \backslash in\; \backslash R^$ such that $P\; =\; P^T$ and : The corresponding equivalence for strict inequalities holds even if $(A,\; B)$ is not controllable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kalman–Yakubovich–Popov lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.