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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 Additive State Decomposition ： ウィキペディア英語版 Additive State Decomposition Additive state decomposition occurs when a system is decomposed into two or more subsystems with the same dimension as that of the original system. A commonly-used decomposition in the control field is to decompose a system into two or more lower-order subsystems, called lower-order subsystem decomposition here. In contrast, additive state decomposition is to decompose a system into two or more subsystems with the same dimension as that of the original system. Taking a system for example, it is decomposed into two subsystems: and , where and , respectively. The lower-order subsystem decomposition satisfies : $n\; =\; n\_\; +\; n\_\backslash text\; P\; =\; P\_\; \backslash oplus\; P\_$ By contrast, the additive state decomposition satisfies : $n\; =\; n\_\; =\; n\_\; \backslash text\; P\; =\; P\_\; +\; P\_$ ==Additive state decomposition on a dynamical control system== Consider an ‘original’ system as follows: where $x\backslash in\backslash R^n$. First, a ‘primary’ system is brought in, having the same dimension as the original system: where $x\_\backslash in\backslash R^n.$ From the original system and the primary system, the following ‘secondary’ system is derived: : $\backslash dot\; -\; \backslash dot\_\; =\; f(t,x,u)\; -\; f\_\; (t,x\_,u\_),\; x(0)\; =\; x\_$ New variables $x\_\backslash in\backslash R^n$ are defined as follows: Then the secondary system can be further written as follows: From the definition (), it follows : $x(t)=x\_(t)+x\_(t),$ $t\backslash geq\; 0.$ The process is shown in this picture: 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「Additive State Decomposition」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.