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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 Observability Gramian ： ウィキペディア英語版 Observability Gramian The Observability Gramian is a Gramian used in optimal control theory to determine whether or not a linear system is observable. For a linear system described by $\backslash dot(t)\; =\; A(t)\; x(t)\; +\; B(t)\; u(t)$ $y(t)\; =\; C(t)\; x(t)\; +\; D(t)\; u(t)\; \backslash ,$ The observability Gramian for a linear time variant system is given by $W\_(t\_,t\_)=\backslash int\_\}\backslash Phi^(s,t\_)C^(s)C(s)\backslash Phi(s,t\_)\; ds$ , where $\backslash Phi$ is the state transition matrix. The system is observable on the interval $t\backslash in()$ if and only if $W\_(t\_,t\_)$ is nonsingular. In the case of a linear time invariant system, this can be simplified to finding the rank of the "observability matrix". If $x(t)$ is a $n$-dimensional real-valued vector, then the system is observable if and only if $\backslash text()=n$ ==See also== *Observability *Controllability Gramian *Gramian matrix 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「Observability Gramian」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.