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Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem

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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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Authors and Affiliations

  1. Russian State University of Oil and Gas, Moscow, Russia

    O. O. Vasil’ev, N. I. Osetinskii & F. S. Vainshtein

  2. Georgia Institute of Technology, Atlanta, USA

    O. O. Vasil’ev, N. I. Osetinskii & F. S. Vainshtein

Authors
  1. O. O. Vasil’ev
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  2. N. I. Osetinskii
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  3. F. S. Vainshtein
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Additional information

Original Russian Text © O.O. Vasil’ev, N.I. Osetinskii, F.S. Vainshtein, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 12, pp. 1748–1755.

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Vasil’ev, O.O., Osetinskii, N.I. & Vainshtein, F.S. Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem. Diff Equat 45, 1783–1790 (2009). https://doi.org/10.1134/S001226610912009X

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  • DOI: https://doi.org/10.1134/S001226610912009X

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