Feedback problem...

So there's a feedback connection between G(s) = 1/(1 + s)^2 and a nonlinear function/map psi(t, y) = a*y*sin(w*t). How can I use the small gain theorem to find conditions on "a" so that this connection is finite gain L-infinity stable?

I'm pretty sure I need to use the peak-to-peak gain of G(s), but I'm not sure how to find its impulse response, or what to do about getting the infinity norm of psi.

I'm not sure I understand the feedback. s is the input and y is the output? If so, do is it like:

s -> G(s) -> y
....| ........ |
.....psi(y,t)

Exactly.