Group decision making with multiple leaders: local rules, weighted networks and consensus. (6th November 2008) - Chen, Fei; Chen, Zengqiang; Liu, Zhongxin; Xiang, Linying; , Zhuzhi Yuan
In this paper, a realistic and simple discrete-time model based on nearest neighbour rules for describing the movements of autonomous agents is introduced. Two kinds of networks are considered here: weighted directed networks with fixed topology; weighted directed networks with switching topology. The analysis is based on a blend of graph-theoretic and system-theoretic tools. In addition to the stability analysis, the steady state of convergence is also analysed. It turns out that homogenous digraphs plays a central role in addressing average-consensus problems, where the notation 'leadership' is introduced to measure the influence of a node to the consensus of the group. Finally, numerical examples are included which find very good agreements with the analytical results.