Talk:Small-gain theorem
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[edit]Hi!
Theorem. Assume two systems S1 and S2 are connected in a feedback loop, then the closed loop system is input-output stable iff |S1|*|S2|<1
I dispute the 'iff' in this statement, it should be a simple 'if'. It is very possible for a closed-loop system to be input-output stable where |S1|*|S2|>1
This is really covered in the first paragraph, it says "The small-gain theorem gives a sufficient condition for finite-gain stability of the feedback connection"
Necessary and sufficient means you use iff sufficient means you use if
as far as I understand, anyways! —Preceding unsigned comment added by 99.255.56.16 (talk) 03:33, 4 August 2009 (UTC)
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[edit]Yeah, I agree, it should be "if". I've changed it.
Also: there are other versions of the small gain theorem for different types of system, but this is the most commonly cited one. —Preceding unsigned comment added by 155.198.165.46 (talk) 12:12, 11 August 2009 (UTC)