math attack : feedback

[Martin Czech]

If several bandpass sections are cascaded, and a feedback path
goes from the last one back to the first, there is pole spread out.
It is easy to show that the zeros stay at 0 (well, not exactly, we
allready had that). I've looked at 2-8nd order, only one pole
pair comes closer to the jw axis and will finally lead to oscillation.
All other poles stay away.

Why is this so, I mean, is there a fundamental mathematical
theorem behind that?

>From the measurement point of view we can say that a distinct
oscillation is reached at some point, so a single pole pair
makes sense, of course. However, I could imagine that more
characteristic frequencys are possible.

m.c.