Abstract

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. Specifically, we provide necessary and sufficient conditions, based on simple rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph is reachable (observable) from any single node if and only if the number of nodes of the graph is a power of two, n = 2^i; i in N, and (ii) a cycle is reachable (observable) from any pair of nodes if and only if n is a prime number. For any set of control (observation) nodes, we provide a closed form expression for the (unreachable) unobservable eigenvalues and for the eigenvectors of the (unreachable) unobservable subsystem.

Autore Pugliese

• Parlangeli Gianfranco , Notarstefano Giuseppe

Tutti gli autori

• Parlangeli G. , Notarstefano G.

Titolo volume/Rivista

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Anno di pubblicazione

2012

ISSN

0018-9286

ISBN

Non Disponibile

Numero di citazioni Wos

71

Ultimo Aggiornamento Citazioni

27/04/2018

Numero di citazioni Scopus

88

Ultimo Aggiornamento Citazioni

26/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile