An analytic stability test for a class of time-delay systems

Stability properties of linear dynamic systems with characteristic equations of the form
\Sigma\min{i=0}\max{n} P_{i}(s)e^{-shi}=0
, where all the polynomials P
i
are of order
\leq r
in
s
, can be determined from a polynomial equation in
s
of order
\leq 2n + r
.