# A matrix inequality based design method for consensus problems in multi-agent systems

Shohei Okuno; Joe Imae; Tomoaki Kobayashi

International Journal of Applied Mathematics and Computer Science (2009)

- Volume: 19, Issue: 4, page 639-646
- ISSN: 1641-876X

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topShohei Okuno, Joe Imae, and Tomoaki Kobayashi. "A matrix inequality based design method for consensus problems in multi-agent systems." International Journal of Applied Mathematics and Computer Science 19.4 (2009): 639-646. <http://eudml.org/doc/207962>.

@article{ShoheiOkuno2009,

abstract = {In this paper, we study a consensus problem in 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. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.},

author = {Shohei Okuno, Joe Imae, Tomoaki Kobayashi},

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

keywords = {multi-agent systems; consensus; decentralized control; graph Laplacian; matrix inequality; LMI},

language = {eng},

number = {4},

pages = {639-646},

title = {A matrix inequality based design method for consensus problems in multi-agent systems},

url = {http://eudml.org/doc/207962},

volume = {19},

year = {2009},

}

TY - JOUR

AU - Shohei Okuno

AU - Joe Imae

AU - Tomoaki Kobayashi

TI - A matrix inequality based design method for consensus problems in multi-agent systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2009

VL - 19

IS - 4

SP - 639

EP - 646

AB - In this paper, we study a consensus problem in 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. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.

LA - eng

KW - multi-agent systems; consensus; decentralized control; graph Laplacian; matrix inequality; LMI

UR - http://eudml.org/doc/207962

ER -

## References

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