Comments on "Convexity of frequency response arcs associated with a stable polynomial

In the original paper, Hamann and Barmish (ibid., vol. 38, no. 6, p. 904-15, 1993) showed that the frequency response arc and the inner frequency response set associated with D-stable polynomial are convex. This note points out that clockwise property and positive curvature is sufficient for convexity based on a result in classical differential geometry and provides an alternative proof of the convexity based on curvature. It is felt that this line of proof may be more easily generalized to study the rational function cases. >