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This paper presents a robust control strategy for tracking sinusoidal reference signals with zero steady state error and harmonic compensation in Uninterruptible Power Supplies - UPS. Multiple resonant controllers are derived for DC-AC inverters when supplying energy to (uncertain) nonlinear loads to obtain a nice tradeoff between transient response and disturbance rejection regardless possible load variations. The controller parameters are determined by means of a convex optimization problem subject to a set of linear matrix inequalities (LMIs). Real time experiments demonstrate the potentials of the proposed approach for controlling UPS systems.