翻訳と辞書 Words near each other ・ Fractional ownership of aircraft ・ Fractional part ・ Fractional Poisson process ・ Fractional programming ・ Fractional quantum Hall effect ・ Fractional quantum mechanics ・ Fractional renting ・ Fractional rig ・ Fractional Schrödinger equation ・ Fractional sodium excretion ・ Fractional supersymmetry ・ Fractional vortices ・ Fractional wavelet transform ・ Fractional-order control ・ Fractional-order integrator ・ Fractional-order system ・ Fractional-reserve banking ・ Fractionalism ・ Fractionalization ・ Fractionated spacecraft ・ Fractionating column ・ Fractionation ・ Fractionation Research Inc. ・ Fractionism ・ FractMus ・ Fractofusus misrai ・ Fractography ・ Fractolatirus ・ Fractolatirus normalis ・ Fracton Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fractional-order system ： ウィキペディア英語版 Fractional-order system In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. Fractional-order systems are useful in studying the anomalous behavior of dynamical systems in electrochemistry, biology, viscoelasticity and chaotic systems.〔 == Definition == A general dynamical system of fractional order can be written in the form : $H(D^)(y\_1,y\_2,\backslash ldots,y\_l)\; =\; G(D^)(u\_1,u\_2,\backslash ldots,u\_k)$ where $H$ and $G$ are functions of the fractional derivative operator of orders $\backslash alpha\_1,\backslash alpha\_2,\backslash ldots,\backslash alpha\_m$ and $\backslash beta\_1,\backslash beta\_2,\backslash ldots,\backslash beta\_n$ and $y\_i$ and $u\_j$ are functions of time. A common special case of this is the linear time-invariant (LTI) system in one variable: : $\backslash left(\backslash sum\_^m\; a\_k\; D^\backslash right)\; y(t)\; =\; \backslash left(\backslash sum\_^n\; b\_k\; D^\backslash right)\; u(t)$ The orders $\backslash alpha\_k$ and $\backslash beta\_k$ are in general complex quantities, but two interesting cases are when the orders are ''commensurate'' : $\backslash alpha\_k,\; \backslash beta\_k\; =\; k\; \backslash delta,\; \backslash quad\; \backslash delta\; \backslash in\; R^+$ and when they are also ''rational'': : $\backslash alpha\_k,\; \backslash beta\_k\; =\; k\; \backslash delta,\; \backslash quad\; \backslash delta\; =\; \backslash frac,\; q\; \backslash in\; Z^+$ When $q=1$, the derivatives are of integer order and the system becomes an ordinary differential equation. Thus by increasing specialization, LTI systems can be of general order, commensurate order, rational order or integer order. 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「Fractional-order system」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.