Phase properties of Hurwitz polynomials

Rantzer (1992) established a fundamental bound on the rate of change of phase of a Hurwitz polynomial. An inductive proof was given. Bose (1994) stated that this fundamental bound can be derived from Tellegen´s theorem in network theory. The purpose of this paper is to give a direct proof of the fundamental bound using the Hermite-Bieler theorem which in turn follows from the monotonic phase property and total phase change properties of a Hurwitz polynomial. This is instructive because control engineers are, by and large, unfamiliar with Tellegen´s theorem and our direct proof makes transparent the central role played by these phase properties