The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Controllability and Observability of Grid Graphs via Reduction and Symmetries
Open accessAbstract
In this paper, we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in network control and estimation, quantum computation and discretization of partial differential equations. Specifically, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable (observable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the controllability (respectively, observability) analysis of the grid.
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Cites
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522 · cited 1×
“A survey on these algorithms and their performance may be found in [9] and references therein.”
BackgroundGraph Theoretic Methods in Multiagent Networks
Mesbahi, M., & Egerstedt, M. (2010) · Princeton University Press eBooks · doi:10.1515/9781400835355 · Cited by 2,897 · cited 1×
““necessary and sufficient” conditions are provided to characterize the controllability and observability of path and cycle graphs in terms of simple rules from number theory. In [8] and [9], see also [10], necessary conditions for controllability, based on suitable properties of the graph, are provided. Other contribut…”
BackgroundQuantum random walks: An introductory overview
Kempe, J. (2003) · Contemporary Physics · doi:10.1080/00107151031000110776 · Cited by 1,413
Cited by
Controllability Metrics, Limitations and Algorithms for Complex Networks
Pasqualetti, F., Zampieri, S., & Bullo, F. (2014) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2014.2310254 · Cited by 594
Exact controllability of complex networks
Yuan, Z., Zhao, C., Di, Z., Wang, W.-X., & Lai, Y.-C. (2013) · Nature Communications · doi:10.1038/ncomms3447 · Cited by 565
Synchronization in complex networks and its application – A survey of recent advances and challenges
Tang, Y., Qian, F., Gao, H., & Kurths, J. (2014) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2014.09.003 · Cited by 358
Metadata
- Authors
- Notarstefano, G., & Parlangeli, G.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2013-07
- Volume
- 58
- Issue
- 7
- Pages
- 1719-1731
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2168109446
- Cited by
- 171
- References
- 3
- FWCI
- 23.89
- Type
- journal article
- Language
- en
- Open access
- green
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- Notarstefano, G., & Parlangeli, G. (2013). Controllability and Observability of Grid Graphs via Reduction and Symmetries. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2013.2241493
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