### Abstract

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

Original language | English |
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Title of host publication | 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program |

Pages | 529-533 |

Number of pages | 5 |

Publication status | Published - 2011 |

Event | 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Zhengzhou Duration: 2011 Aug 11 → 2011 Aug 13 |

### Other

Other | 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 |
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City | Zhengzhou |

Period | 11/8/11 → 11/8/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Mechanical Engineering

### Cite this

*2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program*(pp. 529-533). [6024950]

**A notion of generalized graph Laplacian and its application to distributed consensus algorithm.** / Zhai, Guisheng.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program.*, 6024950, pp. 529-533, 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011, Zhengzhou, 11/8/11.

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TY - GEN

T1 - A notion of generalized graph Laplacian and its application to distributed consensus algorithm

AU - Zhai, Guisheng

PY - 2011

Y1 - 2011

N2 - In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

AB - In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

KW - adjacency weights

KW - cooperative control

KW - distributed consensus algorithm

KW - generalized graph Laplacian

KW - graph Laplacian

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M3 - Conference contribution

AN - SCOPUS:80053604720

SN - 9780955529375

SP - 529

EP - 533

BT - 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program

ER -