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A combinatorial approach to the (positive) reachability of 2D positive systems

Local reachability of two-dimensional (2D) positive systems, by means of positive scalar inputs, is addressed. The combinatorial nature of this property allows for a graph theoretic approach. Indeed, to every 2D positive system of dimension n with scalar inputs one can associate a 2D influence graph with n vertices, one source and two types of arcs interconnecting the source and the vertices. Some results concerned with equivalent conditions for local reachability as well as upper and lower bounds on the reachability indices are provided.