An Internal Model Principle for Synchronization

The problem of achieving synchrony in a group of heterogeneous systems is considered. By synchrony, we understand the fact of temporal coincidence of output trajectories of the individual systems. The individual systems are modeled as general time-invariant nonlinear systems which are coupled through relative error measures. The question is addressed, what properties the individual systems need to possess if there exists a solution to the synchronization problem. An answer to that question is given in the form of an internal model principle for synchronization representing a necessary condition for synchronization.