Global synchronization of networked systems with bidirectional connections

This paper studies the global synchronization problem of networked systems with bidirectional connections. We introduce a virtual node to produce the reference trajectory which will track the average state of network and eventually run in an interesting domain. The concept of synchronous degree of vector filed over domain is presented to derive a simple synchronous criterion. This criterion clearly states the actions on synchronizability of the nodal self-dynamics and the coupling matrix of network, and can be directly extended to the case of switching topology. Examples and numerical simulations illustrate the efficacy of the developed results.