Edge agreement: Graph-theoretic performance bounds and passivity analysis

Daniel Zelazo, Mehran Mesbahi

Research output: Contribution to journalArticlepeer-review


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, provides a useful perspective on the well-known node agreement, or the consensus algorithm. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role of certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. Using the edge Laplacian, we proceed to examine graph-theoretic characterizations of the ℋ2 and ℋ performance for the agreement protocol. These results are subsequently applied in the contexts of optimal sensor placement for consensus-based applications. Finally, the edge Laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics.

Original languageEnglish
Article number5504814
Pages (from-to)544-555
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 2011
Externally publishedYes


  • Agreement protocol
  • consensus
  • networked dynamic systems
  • passivity

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


Dive into the research topics of 'Edge agreement: Graph-theoretic performance bounds and passivity analysis'. Together they form a unique fingerprint.

Cite this