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- Small-gain_theorem abstract "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 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 and 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).".
- Small-gain_theorem wikiPageID "16696745".
- Small-gain_theorem wikiPageRevisionID "582157593".
- Small-gain_theorem hasPhotoCollection Small-gain_theorem.
- Small-gain_theorem subject Category:Nonlinear_control.
- Small-gain_theorem comment "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 stability of the feedback connection. The small gain theorem was proved by George Zames in 1966.".
- Small-gain_theorem label "Small-gain theorem".
- Small-gain_theorem label "Twierdzenie o małym wzmocnieniu".
- Small-gain_theorem label "مبرهنة التقوية الصغيرة".
- Small-gain_theorem sameAs Twierdzenie_o_małym_wzmocnieniu.
- Small-gain_theorem sameAs m.03yndj0.
- Small-gain_theorem sameAs Q4165677.
- Small-gain_theorem sameAs Q4165677.
- Small-gain_theorem wasDerivedFrom Small-gain_theorem?oldid=582157593.
- Small-gain_theorem isPrimaryTopicOf Small-gain_theorem.