Positive transfer functions and convex optimization

Recently, a compact characterization of scalar positive polynomials on the real line and on the unit circle was derived by Nesterov [3]. In this paper we show how to extend this result to pseudo-polynomial matrices, and also present a new proof based on the positive real lemma. The characterization is very similar to the scalar case and also allows the use of fast algorithms for computing the central point of the corresponding convex set.