Monomial decomposition of reachable and controllable positive linear systems

An algorithm for decomposing positive linear systems into monomial components is developed for the case when the system matrix contains zero columns. Criteria in digraph form for identifying the reachability and controllability properties of such systems are provided. The decomposition algorithm can be, used to generate a variety of reachable and controllable canonical form of positive linear systems. The graph-theoretic nature of the algorithm substantially simplifies the solution of large-scale problems arising in many application areas of positive systems.