The design and experimental validation of a robust feedback controller for three-phase grid-tied inverters using LCL filter are presented in this paper. The proposed controller is developed in the natural reference frame to deal with normal and abnormal grid voltage conditions. The objective of the proposed controller is to achieve the goals of stabilization, accurate tracking of sinusoidal references, and asymptotic disturbance rejection. These goals are fulfilled by considering an existing dynamic/stabilizing compensator, which was proposed for a class of perturbed linear systems with sinusoidal disturbances. This compensator guarantees accurate sinusoidal reference tracking under fixed-frequency sinusoidal disturbances. However, during the saturation of control input, the transient response can be deteriorated due to the resonant build-up and can even destroy the closed-loop stability. To overcome this issue, the dynamic compensator is modified, in this paper, to incorporate an anti-windup scheme, where the gain is determined using absolute stability tools including the circle criterion. The proposed controller demonstrated a strong ability to ensure exact tracking of the sinusoidal current reference and reject sinusoidal disturbances with a good transient response even when the momentarily controller saturates.