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For a droop-controlled micro-grid, it is essential to design the droop coefficients for the inverter controllers in a rational way since they have great influences on the operation characteristics of the system. In this paper, a novel approach based on matrix perturbation theory is proposed for the coordinated optimization of the droop coefficients in inverter controllers. Rigorous perturbation analysis is applied to the droop coefficients to identify their influence on the system state matrix. Furthermore, the increments of the eigensolutions are obtained based on the matrix perturbation theory and are then utilized in the iterative parameter-optimization process. An eigenvalue-based objective function is proposed, aimed at ensuring the stability of the system, enhancing the damping characteristics, and maintaining the stability margin for a wide range of operating conditions. Finally, the effectiveness and robustness of the proposed approach are tested via a low-voltage micro-grid prototype.