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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 Flatness (systems theory) ： ウィキペディア英語版 Flatness (systems theory) Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a ''flat system''. Flat systems have a (fictitious) ''flat output'', which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives. Flatness in systems theory is based on the mathematical notion of flatness in commutative algebra and is applied in control theory. == Definition == A nonlinear system $\backslash dot(\backslash mathbf(t),\backslash mathbf(t)),\; \backslash quad\; \backslash mathbf(0)\; =\; \backslash mathbf\_0,\; \backslash quad\; \backslash mathbf(t)\; \backslash in\; R^m,\; \backslash quad\; \backslash mathbf(t)\; \backslash in\; R^n,\; \backslash text\; \backslash frac,\backslash mathbf)\}(t)\; =\; (y\_1(t),...,y\_m(t))$ that satisfies the following conditions: * The signals $y\_i,i=1,...,m$ are representable as functions of the states $x\_i,i=1,...,n$ and inputs $u\_i,i=1,...,m$ and a finite number of derivatives with respect to time $u\_i^,\; k=1,...,\backslash alpha\_i$: $\backslash mathbf\; =\; \backslash Phi(\backslash mathbf,\backslash mathbf,\backslash dot^)$. * The states $x\_i,i=1,...,n$ and inputs $u\_i,i=1,...,m$ are representable as functions of the outputs $y\_i,i=1,...,m$ and of its derivatives with respect to time $y\_i^,\; i=1,...,m$. * The components of $\backslash mathbf$ are differentially independent, that is, they satisfy no differential equation of the form $\backslash phi(\backslash mathbf,\backslash dot^)\; =\; \backslash mathbf$. If these conditions are satisfied at least locally, then the (possibly fictitious) output is called ''flat output'', and the system is ''flat''. 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「Flatness (systems theory)」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.