Passivity based state synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols

This paper studies state synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling (i.e., agents are coupled through part of states). We identify three classes of agents, for which static linear protocols can be designed. They are agent which are squared-down passive, squared-down passifiable via output feedback, or G-minimum-phase with relative degree 1. We find that, for squared-down passive agents, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree, while for the other two classes of agents, the static protocol needs rough information on the network graph, in particular, a lower bound of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network is no longer needed for the other two classes of agents.