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This paper presents a new predictive current control for three-phase grid-connected inverters in the synchronous reference frame. The control combines a deadbeat control law with a diagonal Luenberger observer to estimate the future value of the grid currents. It provides a decoupled control of the active and reactive power and offers robustness against the computational delay inherent in the digital implementation and against filter and grid-impedance uncertainties. This control exhibits a very fast current response while widely improving the gain and phase margins of the traditional predictive controllers.