Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem
O. O. Vasil’ev, N. I. Osetinskii, F. S. Vainshtein · Differential Equations · 2009
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.