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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 Small-gain theorem ： ウィキペディア英語版 Small-gain theorem In nonlinear systems, the formalism of input-output stability is an important tool in studying the stability of interconnected systems since the gain of a system directly relates to how the norm of a signal increases or decreases as it passes through the system. The small-gain theorem gives a sufficient condition for finite-gain $\backslash mathcal$ stability of the feedback connection. The small gain theorem was proved by George Zames in 1966. It can be seen as a generalization of the Nyquist criterion to non-linear time varying MIMO systems (systems with multiple inputs and multiple outputs). ''Theorem''. Assume two stable systems $S\_1$ and $S\_2$ are connected in a feedback loop, then the closed loop system is input-output stable if . (The norm can be the infinity norm, that is the size of the largest singular value of the transfer function over all frequencies. Also any induced Norm will lead to the same results).〔Glad, Ljung: Control Theory, Page 19〕〔Glad, Ljung: Control Theory (Edition 2:6), Page 31〕 == Notes == 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「Small-gain theorem」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.