This paper discusses a systematic control design for a three-phase L-filtered grid-connected inverter using linear matrix inequality-based optimization method. A state feedback control is employed to provide stability to the inverter system and with the inclusion of integral control the offset error can be eliminated. In addition, the proposed control is implemented in dq-synchronous frame with help from a phase locked-loop to track the grid phase angle. The optimization criterion of this proposed control is to reduce the convergence time to the steady state as short as possible. The set of robust stabilizing gain is systematically discussed in this paper and computed using MATLAB toolbox. Then, the effectiveness of this proposed control algorithm is verified by implementing on PSIM simulation tool.