Structural properties of 2D positive state-space models

When dealing with two-dimensional (2D) discrete state-space models, reachability and observability are introduced in two different forms: a local form, which refers to single local states, and a global form, which instead pertains the infinite set of local states lying on a separation set. In this paper, these concepts are in- troduced and investigated in the context of 2D positive systems. Necessary and sufficient conditions for the ex- istence of these properties are provided and, in partic- ular, canonical forms for globally reachable/observable positive systems with scalar inputs/scalar outputs are provided.