Positive Linear Systems Reachability Criterion in Digraph Form

Abstract

Reachability criterion in digraph form for discrete-time positive linear systems in terms of the non-negative pair (A, B) is obtained. The criterion (and the proof) is based on a simple (vertex) decomposition of the system matrix digraph into monomial subdigraphs: simple monomial paths, blossoms, cycles, monomial trees and bunches. The reachability criterion gives not only a deeper insight into the structure of reachable positive systems but its graph theoretic nature makes it easy to solve large-scale problems.