A Katz-centrality-based protocol design for leader-following formation of discrete-time multi-agent systems with communication delays

This paper aims at constructing an improved structure for the consensus protocol in discrete-time multi-agent systems. A consensus protocol is proposed by using the centrality measure for agent which is determined by the information flow through multi-agent systems. In analyzing multi-agent systems, a graph representation is used. The concept of centrality measure which was introduced in the field of social network analysis is attempted to find the most central node within the graph. This work is intended to observe the Katz-centrality that is one of centrality measures. Here, the advantage of Katz-centrality is that a node's centrality depends not only on how many others the node is connected to (its degree), but also on their centrality. The alternative consensus protocol will be applied to the leader-following formation problems for discrete-time multi-agent systems with second-order dynamics and time-varying communication delay. To achieve this, sufficient conditions for the aforementioned problems will be established in terms of linear matrix inequality by utilizing the Lyapunov method and some mathematical techniques. Finally, the discrete-time multi-agent systems modeled with a point-mass dynamics of motion for aircraft and its simulation results are given to illustrate the advantages of the alternative consensus protocol in point of the robustness on time delay and H∞ performance.