Global State Synchronization in Networks of Cyclic Feedback Systems

This technical note studies global asymptotic state synchronization
in networks of identical systems. Conditions on the coupling
strength required for the synchronization of nodes having a cyclic feedback
structure are deduced using incremental dissipativity theory. The
method takes advantage of the incremental passivity properties of the
constituent subsystems of the network nodes to reformulate the synchronization
problem as one of achieving incremental passivity by coupling.
The method can be used in the framework of contraction theory to
constructively build a contracting metric for the incremental system. The
result is illustrated for a network of biochemical oscillators.