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Practice Question on System Stability
The input x(t) and the output y(t) of a system are related by the equation
$ y(t)=\frac{1}{1+x^2(t)}. $
Is the system stable? Answer yes/no and ustify your answer.
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
This system is stable. I'm actually not sure how to show this, does the following logic work?
$ \lim_{x(t) \to 0}\frac{1}{1+x^2(t)} = 1 $ and $ \frac{1}{1+x^2(t)} < 1 $ for all x(t), thus the system is stable.
I'm not sure that the justification works here...
--Cmcmican 17:44, 24 January 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
