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.