Convexity of a frequency response are associated with a stable entire function

In this paper the authors extend the convexity results for Hurwitz polynomials reported in Hamann and Barmish (1993) to a large class of entire functions. This class includes all the Hurwitz quasi-polynomials. The authors show that the origin may fail to be in the interior of the inner frequency response set of a Hurwitz quasi-polynomial and state a sufficient condition which prevents this from happening.