Consensus and synchronization of linear high-order systems via output coupling

In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. In particular, it is shown that consensus is reached when the information processing filter k(s) is designed so that it stabilizes λ_ig(s) where g(s) is the dynamics of the agents, and λ_i are the non-zero eigenvalues of the Laplacian representing the communication graph. We also compute the asymptotic trajectory of the agents, which is the outcome of the agreement among the agents, and depends on the initial conditions of the agents. As a showcase, some specific design of k(s) is given for the first-order and the second-order consensus problems, respectively.