Synchronization Condition in Networks of coupled Lur'e Systems with Time-delays

A Graph Structure-based Approach

Abstract

This paper considers a synchronization condition in networks of coupled Lur'e systems with time-delay. In general, the emergence of synchronization in delayed networks depends on the coupling strength and the time-delay between the coupled systems. In this paper, paying attention to eigenvalues of the Laplacian matrix, we show the relationship between the eigenvalues and the synchronization condition for complete graph networks and then attempt to generalize the criterion for more general graph networks.