Dynamic feedback synchronization of Lur'e networks via incremental sector boundedness

In this note, we generalize our results on synchronization of homogeneous Lur'e networks by static, relative state information based protocols from Zhang et al to the case that for each agent only relative measurements are available. We establish sufficient conditions under which a linear dynamic synchronization protocol exists for such networks. These conditions involve feasibility of two LMI's together with a coupling inequality, reminiscent of the well-known LMI conditions in H-infinity control by measurement feedback. We show that, regardless of the number of agents in the network, only the three inequalities are involved. In the computation of the protocol matrices, the eigenvalues of the Laplacian matrix of the interconnection graph occur. In particular, the matrices representing the protocol depend on the smallest nonzero eigenvalue and the largest eigenvalue of the Laplacian matrix. We validate our results by means of a numerical simulation example