I would like to know what the best method is for finding stability of transfer functions that have internal delays. Basically I have a transfer function of the form:
$\frac{f(s) e^{-st}}{g(s) + h(s) e^{-st}}$
where $f(s), g(s), h(s)$ are rational functions with real coefficients.
I've looked at the Nyquist criterion, but its hard to get it into the necessary form, and I've also looked at Pade approximations. However, there doesn't seem to be any way to validate whether the Pade approximation is accurate enough to give answers on the stability of the transfer function. I've also found some articles on Mikhailov stability criterion, though I'm not sure if its applicable in this case.