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This paper deals with the synthesis problem of multiple resonant controllers for uninterruptible-power-supply systems in a robust control framework. The controller parameters aiming the tracking of sinusoidal reference signals (with zero steady-state error) and the rejection of harmonic components of the output voltage (when supplying energy to time-varying nonlinear loads) are determined by means of a convex optimization problem subject to a set of linear-matrix-inequality constraints. Results from a 5.0-kVA experimental setup are considered to illustrate and validate the proposed approach.