The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to Network-Decentralized Estimation for Homogeneous Systems

Giulia Giordano, Franco Blanchini, Elisa Franco, Vahid Mardanlou, Pier Luca Montessoro

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

The problem of synthesizing network-decentralized 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 network-decentralized 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 so-called 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 worst-case smallest eigenvalue of the generalized Laplacian matrix for externally connected graphs, and we prove that the worst-case graph is a chain. This general result provides a bound for the observer gain that ensures robustness of the network-decentralized observer even under arbitrary, possibly switching, configurations, and in the presence of noise.

Original languageEnglish
Article number7542498
Pages (from-to)312-324
JournalIEEE Transactions on Network Science and Engineering
Volume3
Issue number4
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Keywords

  • generalized Laplacian matrix
  • Graph theory
  • network problems
  • network-decentralized estimation
  • network-decentralized observer

Fingerprint Dive into the research topics of 'The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to Network-Decentralized Estimation for Homogeneous Systems'. Together they form a unique fingerprint.

  • Cite this