A note on the nonnegative realization of rational transfer functions

In the literature, three different types of nonnegative realization problem have been addressed: the nonnegative realization problem for strictly proper rational functions [L. Benvenuti and L. Farina, 2004], the nonnegative realization problem for autonomous behaviors [J.W. Nieuwenhuis, 1998], [M.E. Valcher, 2001] and the K-realization problem [H. Maeda and S. Kodama, 1981]. In this paper these problems are compared and mutually related, and some results obtained within the behavioral setting are applied to the solution of the nonnegative realization problem for rational functions.