In this study, a way to design the optimal weights associated
with edges of undirected graph composed of multi-agent systems is presented.
The optimal weights are designed to make the states of the multi-agent
systems converge to consensus with a fast speed as well as the maximum
communication time-delay can be tolerated. The method used in our research
is based on linear matrix inequality theory. The convergence speed which
is determined by the second-smallest eigenvalue of graph Laplacian matrix
is assumed to be a given value, at the same time the maximum communication
time-delay which is decided by the maximum eigenvalue of Laplacian matrix
can be got. In order to get required second-smallest eigenvalue and optimal
maximum eigenvalue, the order of Laplacian matrix is reduced by variable
decomposition. Moreover, designing the optimal weights is equivalent to
minimizing condition number of a positive-definite matrix. Simulation
results are coincidental with theoretical analysis. PDFFulltextXMLReferencesCitation
How to cite this article
Xiang-Shun Li and Hua-Jing Fang, 2009. Optimal Weights for Consensus of Networked Multi-Agent Systems. Information Technology Journal, 8: 77-82.