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Some remarks on Boolean control systems: Controllability domains and realization theory

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Abstract

We construct a theory of realizations and controllability domains for linear stationary systems in the category of finitely generated free semimodules over a Boolean semiring. We show that the classical realization theorems cannot be generalized to this case, and we prove some incomplete analogs of these theorems. We analyze the structure of controllability domains and the reachability and observability characteristics. In particular, we define a geometric object representing the reachability properties of a system, namely, the generalized reachability topology on the state space.

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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. Texas A&M University-Texarkana, Texarkana, Texas, 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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Original Russian Text © O.O. Vasil’ev, N.I. Osetinskii, F.S. Vainshtein, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 12, pp. 1731–1736.

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Vasil’ev, O.O., Osetinskii, N.I. & Vainshtein, F.S. Some remarks on Boolean control systems: Controllability domains and realization theory. Diff Equat 46, 1731–1736 (2010). https://doi.org/10.1134/S0012266110120062

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  • DOI: https://doi.org/10.1134/S0012266110120062

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