### Abstract

In this paper, we study a consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. Existing approaches in the literature are mostly based on graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods can not deal with complicated control specification. For this purpose, we propose to reduce the consensus problem on hand to solving a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and then propose two algorithms for solving the matrix inequality. It turns out that our approach includes the existing Laplacian based approach as a special case, and can deal with various additional control requirements such as convergence rate specification and actuator limitations.

Original language | English |
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Title of host publication | Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 |

Pages | 891-896 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 - Okayama Duration: 2009 Mar 26 → 2009 Mar 29 |

### Other

Other | 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 |
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City | Okayama |

Period | 09/3/26 → 09/3/29 |

### Fingerprint

### Keywords

- Consensus
- Decentralized state (output) feedback
- Graph laplacian
- Homotopy
- LMI
- Matrix inequality
- Multi-agent systems

### ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009*(pp. 891-896). [4919398] https://doi.org/10.1109/ICNSC.2009.4919398

**Consensus algorithms for multi-agent systems : A matrix inequality based approach.** / Zhai, Guisheng; Okuno, Shohei; Imae, Joe; Kobayashi, Tomoaki.

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

*Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009.*, 4919398, pp. 891-896, 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009, Okayama, 09/3/26. https://doi.org/10.1109/ICNSC.2009.4919398

}

TY - GEN

T1 - Consensus algorithms for multi-agent systems

T2 - A matrix inequality based approach

AU - Zhai, Guisheng

AU - Okuno, Shohei

AU - Imae, Joe

AU - Kobayashi, Tomoaki

PY - 2009

Y1 - 2009

N2 - In this paper, we study a consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. Existing approaches in the literature are mostly based on graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods can not deal with complicated control specification. For this purpose, we propose to reduce the consensus problem on hand to solving a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and then propose two algorithms for solving the matrix inequality. It turns out that our approach includes the existing Laplacian based approach as a special case, and can deal with various additional control requirements such as convergence rate specification and actuator limitations.

AB - In this paper, we study a consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. Existing approaches in the literature are mostly based on graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods can not deal with complicated control specification. For this purpose, we propose to reduce the consensus problem on hand to solving a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and then propose two algorithms for solving the matrix inequality. It turns out that our approach includes the existing Laplacian based approach as a special case, and can deal with various additional control requirements such as convergence rate specification and actuator limitations.

KW - Consensus

KW - Decentralized state (output) feedback

KW - Graph laplacian

KW - Homotopy

KW - LMI

KW - Matrix inequality

KW - Multi-agent systems

UR - http://www.scopus.com/inward/record.url?scp=70349109623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349109623&partnerID=8YFLogxK

U2 - 10.1109/ICNSC.2009.4919398

DO - 10.1109/ICNSC.2009.4919398

M3 - Conference contribution

AN - SCOPUS:70349109623

SN - 9781424434923

SP - 891

EP - 896

BT - Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

ER -