<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.</p></abstract>

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

A generalization of the graph Laplacian with application to a distributed consensus algorithm

Department of Mathematical Sciences Shibaura Institute of Technology, Saitama 337-8570, Japan

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency...

A generalization of the graph Laplacian with application to a distributed consensus algorithm

Published Online: Jun 25, 2015

Page range: 353 - 360

Received: Jan 06, 2014

DOI: https://doi.org/10.1515/amcs-2015-0027

© by Guisheng Zhai

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.