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. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squared-down passive, squared-down passifiable via output feedback, squared-down passifiable via input feedforward and squared-down minimum-phase with relative degree 1. We find that, for agents which are squared-down passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus 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 can be dispensed with. (C) 2018 Elsevier Ltd. All rights reserved.