  Due to its description of a synchronization between oscillators, the Kuramoto
model is an ideal choice for a synchronisation algorithm in networked systems.
This requires to achieve not only a frequency synchronization but also a phase
synchronization - something the standard Kuramoto model can not provide for a
finite number of agents. In this case, a remaining phase difference is
necessary to offset differences of the natural frequencies. Setting the
Kuramoto model into the context of dynamic consensus and making use of the
$n$th order discrete average consensus algorithm, this paper extends the
standard Kuramoto model in such a way that frequency and phase synchronization
are separated. This in turn leads to an algorithm achieve the required
frequency and phase synchronization also for a finite number of agents.
Simulations show the viability of this extended Kuramoto model.
