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

International Journal of Applied Mathematics and Computer Science (2015)

- Volume: 25, Issue: 2, page 353-360
- ISSN: 1641-876X

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topGuisheng Zhai. "A generalization of the graph Laplacian with application to a distributed consensus algorithm." International Journal of Applied Mathematics and Computer Science 25.2 (2015): 353-360. <http://eudml.org/doc/270629>.

@article{GuishengZhai2015,

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.},

author = {Guisheng Zhai},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {graph Laplacian; generalized graph Laplacian; adjacency weights; distributed consensus algorithm; cooperative control},

language = {eng},

number = {2},

pages = {353-360},

title = {A generalization of the graph Laplacian with application to a distributed consensus algorithm},

url = {http://eudml.org/doc/270629},

volume = {25},

year = {2015},

}

TY - JOUR

AU - Guisheng Zhai

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2015

VL - 25

IS - 2

SP - 353

EP - 360

AB - 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.

LA - eng

KW - graph Laplacian; generalized graph Laplacian; adjacency weights; distributed consensus algorithm; cooperative control

UR - http://eudml.org/doc/270629

ER -

## References

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