This paper deals with a novel control architecture for pulse width modulation inverters connected to the grid through resonant LCL filters. A continuous-control-set model predictive control scheme is derived for the grid current loop. A state observer, using a moving horizon estimator algorithm, is used for reducing the order of the mathematical model representing the grid. The proposed control architecture allows for reducing the number of required sensors, for eliminating measurement noise and for achieving a good stability against voltage grid disturbances and parameter uncertainties. High performance hardware is used in order to run a quadratic programming solver in real-time, with a control sampling rate of 10 kHz. The effectiveness of the proposed control architecture is validated by means of test-bed experiments demonstrating the feasibility of real-time operation and promising results.