Synchronization of Oscillators Coupled through a Network with Dynamics: A Constructive Approach with Applications to the Parallel Operation of Voltage Power Supplies

We consider the problem of synchronizing a group of oscillators coupled by a network that is modelled by a multipleinput/multiple-output dynamical system. We provide results that can be used to establish asymptotic synchronization of a given system and also to construct feedback oscillators for which synchronization is guaranteed. These results are based on a new notion of passivity with respect to manifolds defined in the input and output spaces of a dynamical system. The problem under consideration is motivated by the design of high-power electronic inverters that can be used to interface primary energy sources with an AC electrical network. The proposed synchronization strategy is applied to the problem of parallel connected voltage power supplies.