The connection of a DG unit to a weak power system is challenging due to stability issues resulted from dynamic interactions between the DG unit and the grid. LCL-based DG unit is a particularly challenging case due to the presence of a high resonant peak in its frequency response. This paper proposes a robust control strategy to overcome the stability issues of an LCL-based DG unit connected to a weak grid. The main advantage of the proposed control strategy is that it guarantees stability and satisfactory transient performance against the variations of grid impedance. Moreover, it is able to decouple the d- and q channels of the control system which enables independent regulation of the real and reactive output power of the DG unit. Real-time simulations and experimental tests illustrate the effectiveness of the proposed controller in terms of improved transient performance, robust stability, and satisfactory controller set-point tracking.