State models and asymptotic behavior of 2D positive systems

Homogeneous 2D positive systems are 2D state-space models whose variables are alwalys nonnegative and, consequently, are described by a pair of nonnegative square matrices (A, B). In the paper, the properties of these pairs are discussed both in the general case and under particular assumptions like finite memory, separability, and property L. Various aspects of the positive asymptotic dynamic are considered; in particular, sufficient conditions are provided guaranteeing that the local states are eventually strictly positive. Finally, some results on the convergence of the states towards a constant asymptotic distribution are presented.