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 language | English (US) |
|---|---|
| Title of host publication | Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC |
| Pages | 2309-2314 |
| Number of pages | 6 |
| DOIs | |
| State | Published - Dec 1 2007 |
| Event | 46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007 |
Publication series
| Name | Proceedings of the IEEE Conference on Decision and Control |
|---|---|
| ISSN (Print) | 0191-2216 |
Other
| Other | 46th IEEE Conference on Decision and Control 2007, CDC |
|---|---|
| Country | United States |
| City | New Orleans, LA |
| Period | 12/12/07 → 12/14/07 |
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