Higher penetration of renewable energy into the electrical grids using grid-connected converters requires robust control schemes to ensure the stable behavior of these converters during disturbances on the grid side. This paper proposes a robust H∞ control scheme reinforced by the D-stability technique using linear matrix inequality (LMI) approach for a three-phase two-level grid-connected converter with LCL filter. The design performance is validated both by simulations and experimental tests. The results indicate that the H∞ control provides better response during disturbances in the grid such as variations in the grid voltage and short-circuit faults when compared to that of the conventional vector control scheme. An experimental validation is carried out by implementing the control scheme on an OPAL-RT-based realtime system to control the power injection of a grid-connected converter hardware setup. The experimental results match the simulation results and show the efficient performance of the proposed control scheme in providing the desired active/reactive power.