Synchronizable nodes in networked systems

Synchronization appears in networked systems as a phenomenon of interacting nodes. The notion of synchronizability describes the property that the nodes can be forced to a synchronous behaviour by an appropriate interconnection structure. Whereas in earlier papers synchronizability has been investigated in terms of both the properties of the nodes and of the interconnection topology, this paper shows that for linear coupled systems, synchronizability is a property of the node dynamics alone. If the nodes do not satisfy the necessary and sufficient synchronizability condition derived, no interaction structure can ensure a synchronous behaviour of the networked system. On the other hand, if this condition is satisfied, several interconnection structures given in this paper ensure synchronism globally in the whole state space.