<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan

International Journal of Applied Mathematics and Computer Science

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...

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

Published Online: Dec 31, 2009

Page range: 639 - 646

DOI: https://doi.org/10.2478/v10006-009-0051-1

Keywords
multi-agent systems, consensus, decentralized control, graph Laplacian, matrix inequality, LMI

This content is open access.

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

Published Online: Dec 31, 2009

Page range: 639 - 646

DOI: https://doi.org/10.2478/v10006-009-0051-1

Keywordsmulti-agent systems, consensus, decentralized control, graph Laplacian, matrix inequality, LMI

This content is open access.

Keywords
multi-agent systems, consensus, decentralized control, graph Laplacian, matrix inequality, LMI