This paper presents a voltage controller design of three-phase voltage source inverters using LQR-based active damping and H∞ control strategy. Active damping consists of an LQR voltage and current feedback of LC filter in the αβ frame. In addition to the damping obtained in the LC filter, the proposed LQR strategy allows increasing the bandwidth of the system to reject high frequency disturbances. Three-phase voltage regulation is achieved in the αβ frame using the H∞ control strategy. In this strategy is used a new four order sensitivity functions to obtain very low tracking error and rejection of harmonic disturbances generated by nonlinear loads. The controller has been validated in laboratory tests using 2kW-220V three-phase inverters and non-linear loads. This controller has been compared to resonant proportional control and better performance has been verified. A THD <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> = 1.3% has been experimentally obtained when a nonlinear load is connected.