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This paper presents a current control scheme for a voltage-source converter connected to the grid through an LCL filter. The proposed current control is based on the linear quadratic (LQ) Gaussian (LQG) servo controller technique, which combines the LQ regulator and the Kalman filter (KF). The use of the KF instead of a Luenberger estimator improves the quality of the estimation of state variables in noisy environments, increasing the noise immunity of the control loop. This paper focuses on giving some criteria and practical hints to choose both the KF and LQ design parameters to achieve null steady-state tracking error, channel decoupling, and noise immunity. Furthermore, this paper analyzes the steady-state KF approximation that allows a significant decrement in the computational complexity of the algorithm at nearly no cost in accuracy. Simulation and experimental results prove the correct operation of the proposed LQG current control and the possible advantages of using KF to estimate the state vector.