Motivated by the problem of different types and variations of load in micro-grids, this paper presents robust proportional-resonant controllers with a harmonics compensator based on the internal model principle. These controllers ensure robust tracking of sinusoidal reference signals in distributed energy resource systems subject to load variation with respect to sinusoidal disturbances. The distributed generation resource and the resonant controllers are described using the augmented state system approach, allowing the application of the state feedback technique. In order to minimize the tracking error and ensure robustness against perturbation, a set of linear matrix inequalities (LMIs) are addressed for the synthesizing of controller gains. Finally, results obtained in the simulation for resonant compensators with the distributed energy system are presented, in which the controller is applied to the CC-CA inverter.