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

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Zhai G.

International Journal of Applied Mathematics and Computer Science

2015

tom 25

nr 2

353-360

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.

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1 International Journal of Applied Mathematics and Computer Science

1 Zhai G.

1 2015

Wyniki wyszukiwania

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