In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid or a torus. More in detail, under suitable conditions on the eigenvalue multiplicity, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable (reachable). For any set of observation (leader) nodes, we provide a closed form expression for the unobservable (unreachable) eigenvalues and for the eigenvectors of the unobservable (unreachable) subsystem.

Observability and Reachability of Simple Grid and Torus Graphs

NOTARSTEFANO, Giuseppe;PARLANGELI, GIANFRANCO
2011-01-01

Abstract

In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid or a torus. More in detail, under suitable conditions on the eigenvalue multiplicity, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable (reachable). For any set of observation (leader) nodes, we provide a closed form expression for the unobservable (unreachable) eigenvalues and for the eigenvectors of the unobservable (unreachable) subsystem.
2011
9783902661937
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/363982
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