Lomadze, V, Wood, J and Rogers, E
Singular 2D behaviors: Homologies.
Georgian Mathematical Journal , (1), .
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We present a new definition of a discrete 2D behavior, which generalizes the standard notion by including trajectories from all quarter- and half-planes in Z2. Behaviors then admit certain natural homology spaces, which can be used to define controllability and autonomy, and describe finite trajectories. We discuss the regularity, controllability and autonomy of these models, and demonstrate the equivalence of suitable generalizations of controllability in the senses of Willems and of Rosenbrock, and similarly for autonomy.
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