# Stability varying with order

I have been doing some research into modelling acoustic spaces, and (with help from this site) I've managed to take the frequency response of fibrous layer model, convert it to a reflection response as a target for an IIR, and then find the polynomial coefficients for it using FDLS. All good so far.

I performed the usual BIBO stability test of finding the magnitude of the IIR denominator roots, and with a 4th order filter everything was fine (<=1.0). But increasing the order, even by just one, then it became unstable.

My question is: What does the order actually represent response-wise? I always assumed it determined the sharpest change in direction of the frequency response i.e. the 'jagged-ness' or complexity of the response curve. If that's true, then my filter is unstable, but the few poles I've calculated just happen to be inside the unit circle.

But is that true?