Realization of positive linear systems using polyhedral cones

Positive linear systems are frequently used in research areas like biology and economics. The problem to classify all minimal realizations of these systems is treated in this paper. Extensive use is made of the theory of polyhedral cones. Sufficient and necessary conditions for the existence of a positive realization are given, but the problem of minimality leads to a yet unsolved factorization problem of positive matrices. Ideas and results are given to come towards a solution of this factorization problem