The interaction of droop controllers through power network is high in networked microgrids (NMGs) due to the low X/R ratio of the power lines impedance and lack of inertia in converter-based NMGs, which has raised stability concerns. On the other hand, inaccurate reactive power sharing and poor power quality due to the voltage and frequency deviations still remain as noticeable issues in NMGs. In this paper, a novel fuzzy consensus protocol is proposed to improve the droop controller performance in power sharing by incorporating the X/R ratio of the power lines impedance into droop loops. Power quality is also enhanced by restoring the average voltage profile based on a new consensus protocol, which is designed to be in coordination with reactive power sharing. In order to guarantee stability of the closed-loop system, linear matrix inequality method is adopted to determine the consensus signal coefficients as structured static output feedback gains. To this end, a novel small-signal model is proposed for NMGs to be adopted in the design process, by which the cross-coupling as well as interaction of droop controllers through the power network is properly realized. The numerical results in MATLAB/SIMULINK prove the effectiveness and accuracy of the proposed method.