Information Technology Journal1812-56381812-5646Asian Network for Scientific Information10.3923/itj.2009.77.82LiXiang-Shun FangHua-Jing 1200981In 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.]]>Breder, C.M.,1954Couzin, I.D. and N.R. Franks,2003Couzin, I.D., J. Krause, R. James, G.D. Ruxton and N.R. Franks,2002Cucker, F. and S. Smale,2007Diestel, R.,2000Fax, J.A. and R.M. Murray,2004Hanspeter, K. and K.H. Charlotte,2003Jadbabaie, A., L. Jie and A.S. Morse,2003Moreau, L.,2005Okubo, A.,1986Paganini, F., J. Doyle and S. Low,2001Ren, W. and R.W. Beard,2005Reynolds, C.W.,1987Olfati-Saber, R.,2006Saber, R.O., J.A. Fax and R.M. Murray,2007Olfati-Saber, R. and R.M. Murray,2004Saber, R.O. and R.M. Murray,2003Simon, H., B. Petro, S.T. Sven and G.M. Kjartan,2004Vicsek, T., A. Czirok, E. Ben-Jacob, I. Cohen and O. Sochet,1995Inada, Y.,2001