Agreement via the edge laplacian

Daniel Zelazo, Amirreza Rahmani, Mehran Mesbahi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

40 Scopus citations

Abstract

This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages2309-2314
Number of pages6
DOIs
StatePublished - Dec 1 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Zelazo, D., Rahmani, A., & Mesbahi, M. (2007). Agreement via the edge laplacian. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 2309-2314). [4434553] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434553