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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 Lyapunov equation ： ウィキペディア英語版 Lyapunov equation In control theory, the discrete Lyapunov equation is of the form :$A\; X\; A^\; -\; X\; +\; Q\; =\; 0$ where $Q$ is a Hermitian matrix and $A^H$ is the conjugate transpose of $A$. The continuous Lyapunov equation is of form :$AX\; +\; XA^H\; +\; Q\; =\; 0$. The Lyapunov equation occurs in many branches of control theory, such as stability analysis and optimal control. This and related equations are named after the Russian mathematician Aleksandr Lyapunov. ==Application to stability== In the following theorems $A,\; P,\; Q\; \backslash in\; \backslash mathbb^$, and $P$ and $Q$ are symmetric. The notation $P>0$ means that the matrix $P$ is positive definite. Theorem (continuous time version). Given any $Q>0$, there exists a unique $P>0$ satisfying $A^T\; P\; +\; P\; A\; +\; Q\; =\; 0$ if and only if the linear system $\backslash dot=A\; x$ is globally asymptotically stable. The quadratic function $V(z)=z^T\; P\; z$ is a Lyapunov function that can be used to verify stability. Theorem (discrete time version). Given any $Q>0$, there exists a unique $P>0$ satisfying $A^T\; P\; A\; -P\; +\; Q\; =\; 0$ if and only if the linear system $x(t+1)=A\; x(t)$ is globally asymptotically stable. As before, $z^T\; P\; z$ is a Lyapunov function. 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「Lyapunov equation」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.