Realization of positive linear systems

Abstract Positive linear systems are frequently used as mathematical models in research areas like biology and economics. The problem of classifying 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 the factorization problem for positive matrices. Ideas and results are given to come towards a solution of this factorization problem.

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