Convexity of a frequency response arc associated with a stable quasi-polynomial

We first present a few definitions of frequency response arcs and their argument increase and convexity properties. These definitions are based on the original definitions introduced by Hamann and Barmish (1993). We then reformulate argument increase and arc convexity in terms of certain inner products, which we interpret as first and second angular derivatives. The resulting formulation resembles the first and second derivative test for increase and convexity of real valued functions