Nonnegative realization of a linear system with nonnegative impulse response

Let H(z) be a rational transfer function, with associated nonnegative impulse response sequence. The paper considers the question: When does there exist a triple A∈R^N×N, b∈R ^N, c∈R^N with all nonnegative entries H(z)=c´(zI-A)^-1b? An essentially complete characterization is given of the H(z) allowing such a realization, in terms of the location of the pole or poles of H(z) with maximum modulus