A simple graph theoretic characterization of reachability for positive linear systems |
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Authors: | Christian Commault |
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Affiliation: | aLaboratoire d'Automatique de Grenoble, BP 42, 38402 Saint Martin d'Hères, France |
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Abstract: | In this paper we consider discrete-time linear positive systems, that is systems defined by a pair (A,B) of non-negative matrices. We study the reachability of such systems which in this case amounts to the freedom of steering the state in the positive orthant by using non-negative control sequences. This problem was solved recently Canonical forms for positive discrete-time linear control systems, Linear Algebra Appl., 310 (2000) 49]. However we derive here necessary and sufficient conditions for reachability in a simpler and more compact form. These conditions are expressed in terms of particular paths in the graph which is naturally associated with the system. |
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Keywords: | Linear positive systems Reachability Graph theory |
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