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A robust decentralized control strategy for the islanded operation of a microgrid system is proposed in this paper. The microgrid consists of parallel connection of two electronically-coupled distributed generation (DG) units. The DG units are connected to a point of common coupling (PCC) where a passive load is also connected. In the islanded microgrid, a master DG fulfills voltage and frequency control of the load, and a slave DG utilizes the conventional dq-current control strategy to regulate its power components. It is shown that the parallel connection of two DG units in the islanded mode constitutes an interconnected composite system consisting of two subsystems. Moreover, it is shown that the overall islanded microgrid can be controlled by local controllers, i.e., there is a solution to the robust decentralized servomechanism problem for the composite system. Performance of the proposed control strategy is verified using MATLAB/SimPowerSystems Toolbox.