Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion, and observer design

Abstract

It has been shown that synchronization between two non-linear systems can be studied as a control-theory problem. We show that this relationship can be extended to synchronization in arbitrary coupled arrays of nonlinear systems. In particular, we use several well-known stability conditions to obtain synchronization criteria in arbitrarily coupled arrays: the passivity criterion, the circle criterion and a result on observer design of Lipschitz nonlinear systems. We also study how these synchronization criteria depend on the topology of the coupled networks. In particular, we show that synchronization is improved by using nonlocal connections or introducing random connections.