An Eigenvector-Centrality Based Consensus Protocol Design for Discrete-Time Multi-agent Systems with Communication Delays

Abstract

The leader-follower consensus protocol design problem for a class of discrete-time multi-agent systems (DT-MASs) with the communication delay is addressed in this work, wherein it is assumed that the communication delay is time-varying function. The proposed consensus protocol is substituted by applying the concept of network-centrality for agent, from now on, the protocol will be called to as the substitute consensus protocol. Here, the network-centrality is determined by the flow structure of the information among multiple agents. So, in analyzing the flow structure of the information between each agent, the graph representation is used. In order to find the most influential node, which means agent, within the graph, the various network-centralities have been attempted among the methods of analyzing the social networks. Through this work, we try to take the eigenvector-centrality which is one of network-centralities. Here, its advantage is that the node’s influence is determined by the network-centrality of the node as well as the number of other nodes to which the node is connected. The substitute consensus protocol based on the eigenvector-centrality will be applied to the leader-follower consensus problem for second-order DT-MASs with time-varying communication delay. To do this, by utilizing the Lyapunov method and some mathematical techniques, sufficient conditions for the concerned problem will be proposed in terms of linear matrix inequality. Finally, a point-mass kinematics for aircraft modeled with the DT-MASs and its simulation results are given to verify the advantages of the proposed consensus protocol from a variety of perspective; as an example, the stability in consideration of time-delay.