Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem |
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Authors: | O. O. Vasil’ev N. I. Osetinskii F. S. Vainshtein |
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Affiliation: | (1) Institute of Informatics and Telecommunications, NCSR “Demokritos”, Patriarchou Grigoriou and Neapoleos St. GR-15310, Aghia Paraskevi, Attiki, Greece |
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Abstract: | In the present paper, we consider linear stationary dynamical systems over a Boolean semiring B. We analyze the complete observability, identifiability, reachability, and controllability of such systems. We define the notion of a “graph of modules” of completely controllable, completely reachable Boolean linear stationary systems by analogy with the spaces of modules in the case of systems over fields. We give a graph-theoretic interpretation of systems of this class. We solve the isomorphism problem in this class of systems. |
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