The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to NetworkDecentralized Estimation for Homogeneous Systems
(2016) In IEEE Transactions on Network Science and Engineering 3(4). p.312324 Abstract
 The problem of synthesizing networkdecentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a networkdecentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the socalled generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly... (More)
 The problem of synthesizing networkdecentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a networkdecentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the socalled generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly positive if the graph is externally connected. To deal with uncertain topologies, we characterize the worstcase smallest eigenvalue of the generalized Laplacian matrix for externally connected graphs, and we prove that the worstcase graph is a chain. This general result provides a bound for the observer gain that ensures robustness of the networkdecentralized observer even under arbitrary, possibly switching, configurations, and in the presence of noise. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/e7247903702043d5a06edd1872637709
 author
 Giordano, Giulia ^{LU} ; Blanchini, F.; Franco, Elisa; Mardanlou, V. and Montessoro, P. L.
 organization
 publishing date
 2016
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Eigenvalues and eigenfunctions, Laplace equations, Network topology, Observers, Robustness, Topology, Graph Theory, Network problems, generalized Laplacian matrix, networkdecentralized estimation, networkdecentralized observer
 in
 IEEE Transactions on Network Science and Engineering
 volume
 3
 issue
 4
 pages
 312  324
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 scopus:85012869448
 wos:000409674100010
 ISSN
 23274697
 DOI
 10.1109/TNSE.2016.2600026
 language
 English
 LU publication?
 yes
 id
 e7247903702043d5a06edd1872637709
 date added to LUP
 20161126 14:53:24
 date last changed
 20180313 00:16:59
@article{e7247903702043d5a06edd1872637709, abstract = {The problem of synthesizing networkdecentralized observers arises when several agents, corresponding to the nodes of a network, exchange information about local measurements to asymptotically estimate their own state. The network topology is unknown to the nodes, which can rely on information about their neighboring nodes only. For homogeneous systems, composed of identical agents, we show that a networkdecentralized observer can be designed by starting from local observers (typically, optimal filters) and then adapting the gain to ensure overall stability. The smallest eigenvalue of the socalled generalized Laplacian matrix is crucial: stability is guaranteed if the gain is greater than the inverse of this eigenvalue, which is strictly positive if the graph is externally connected. To deal with uncertain topologies, we characterize the worstcase smallest eigenvalue of the generalized Laplacian matrix for externally connected graphs, and we prove that the worstcase graph is a chain. This general result provides a bound for the observer gain that ensures robustness of the networkdecentralized observer even under arbitrary, possibly switching, configurations, and in the presence of noise.}, author = {Giordano, Giulia and Blanchini, F. and Franco, Elisa and Mardanlou, V. and Montessoro, P. L.}, issn = {23274697}, keyword = {Eigenvalues and eigenfunctions,Laplace equations,Network topology,Observers,Robustness,Topology,Graph Theory,Network problems,generalized Laplacian matrix,networkdecentralized estimation,networkdecentralized observer}, language = {eng}, number = {4}, pages = {312324}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Network Science and Engineering}, title = {The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to NetworkDecentralized Estimation for Homogeneous Systems}, url = {http://dx.doi.org/10.1109/TNSE.2016.2600026}, volume = {3}, year = {2016}, }