Abstract
We consider the problem of synchronizing a group of $N$ identical oscillators, coupled by a symmetric network that is modelled by a multiple-input/multiple-output dynamical system. We provide results that can be used to establish asymptotic synchronization of a given system and also to construct identical 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 control algorithms for the parallel operation of power inverters. Simulation results have shown that synchronization could be achieved in less than two AC cycles, depending on the electrical interconnection network.
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