I realize this is quite basic stuff but I am having trouble with the following question:

Determine whether the following system with input $x(t)$ and output $y(t)$ is BIBO stable: $$y(t) = \frac{1}{x(t)}$$

My intuition says that it is not stable, just from thinking about the case where $x(t) = 0$. However, this would result in $y(t)$ being undefined, not going to infinity. Any help would be appreciated.


1 Answer 1


Hint: define a bound for $|x(t)|$, i.e., $|x(t)|\le A$; now try to find a positive number $B$ such that $|y(t)|\le B$ for any $|x(t)|\le A$ (that's simply the definition of BIBO stability). For the system $y(t)=1/x(t)$ it should be easy to show that the above cannot be satisfied (because $|x(t)|$ can get arbitrarily small).


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