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Singular 2D behaviors: Homologies

Singular 2D behaviors: Homologies
Singular 2D behaviors: Homologies
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.
139-157
Lomadze, V
81f588f3-7588-4777-9052-7116a8c81033
Wood, J
9d32c83e-9d59-4c32-8ab2-a5f64ecc26e6
Rogers, E
611b1de0-c505-472e-a03f-c5294c63bb72
Lomadze, V
81f588f3-7588-4777-9052-7116a8c81033
Wood, J
9d32c83e-9d59-4c32-8ab2-a5f64ecc26e6
Rogers, E
611b1de0-c505-472e-a03f-c5294c63bb72

Lomadze, V, Wood, J and Rogers, E (2008) Singular 2D behaviors: Homologies. Georgian Mathematical Journal, (1), 139-157.

Record type: Article

Abstract

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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More information

Published date: 2008
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 264928
URI: http://eprints.soton.ac.uk/id/eprint/264928
PURE UUID: 85c12cc2-2ba1-479a-8968-c4fb84075cb5
ORCID for E Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 06 Dec 2007 10:35
Last modified: 17 Dec 2019 02:02

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