This paper investigates the control of a four-wire three-phase Uninterruptible Power Supply (UPS) inverter using the internal model principle by applying multiple resonant controllers in the stationary abc-frame for zero-error tracking of sinusoidal reference and harmonic disturbances rejection due to nonlinear and unbalanced loads. The synthesis of such controllers is accomplished in a robust control framework where the controller parameters are determined by means of a convex optimization problem subject to a set of Linear Matrix Inequality (LMI) constraints. Simulation results from a 15.0-kVA UPS inverter are considered to illustrate and validate the performance and behavior of the controller design under nonlinear and unbalanced loads.