I only seem to be able to find online information about applying bilinear transform + pre-warping to filters (like butterworth, etc.) with only one edge frequency that is purposely 'designed' into it. So the BT is easy to apply, just substitute with the usual tangent formula including edge frequency and sampling frequency.
But what if my analog rational transfer function describes a physical system (like an elastic mechanical body with several eigen-frequencies, or an electric circuit network)? Do I have to apply the BT to every pole/zero separately then? And what if the transfer function comes from measurements - I don't know the poles/zeros, because I did not 'design' the 'filter'? Does it really mean I have to factorize it (which we know is sensitive to error) just to transform it from analog to digital?
PS, Sidenote: I am going to implement the numerics involved (in C#) myself. So Matlab is certainly a nice thing, but it does not help me if not all relevant code is publicly available.