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A linear time-invariant (LTI) robust servomechanism controller for islanded (autonomous) operation of a distributed generation (DG) unit and its local load is proposed. The DG unit utilizes a voltage-sourced converter (VSC) as the interface medium. The controller design is obtained by introducing a new optimal controller design procedure, in conjunction with a proposed non-conservative robustness constraint. The proposed controller utilizes 1) an internal oscillator for frequency control and 2) a robust servomechanism controller (RSC) to regulate the island voltage. Despite uncertainty of the load parameters, the proposed controller guarantees robust stability and pre-specified performance criteria, e.g., fast transient response and zero steady-state error. The theoretical aspects of the proposed robust servomechanism controller including the existence conditions, design of the controller, and robust stability analysis of the closed-loop system are studied. Moreover, the performance of the robust servomechanism controller based on 1) simulation studies in the MATLAB software environment, and 2) experiments in a laboratory-scale setup, is presented in this paper. In particular, reference signal tracking and robustness of the closed-loop system with respect to the load parameter uncertainty are investigated. Both computer simulation studies and experimental results confirm that the proposed robust controller provides the specified performance characteristics of the closed-loop system.