I am designing a high-Q analog filter. So, the output response has some ringing by definition and there are going to be high-Q complex conjugate poles.

Now, how does one define stability measures for such a circuit? I am sorry if the question sounds stupid, but there it is.

The one thing I could imagine was comparing the response of the ideal filter (using ideal opamps) to that of the actual realization with real opamps. I anyway need to do that as part of my sensitivity analysis. Here, I could look at the pole/zero locations, even do a Nyquist test by opening various loops one at a time, etc. But I can merely say that the actual transfer function matches the target transfer function with a certain amount of deviation in gain and phase.

However, all this still does not answer my original question viz., definition of stability for a system which is actually expected to ring a bit.

What am I missing?

Thanks
Vivek

I guess what you are concerned with its stability margin. If you do a pz analysis, you can find the quality factor and natural frequency of all pools.  There should be a set of poles close to the desired set in natural frequency and quality factor.  The rest should have a low quality factor and high natural frequency compared to the desired set. That would mean that the response would be close to the desired one.