Abstract: Owing to its good frequency response and inertial support, the virtual synchronous generator (VSG) control strategy has been widely used for inverters in renewable energy generation. However, the voltage droop characteristics may bring about an adverse impact on the transient stability of the VSG. To deal with this issue and provide better reactive power support, a static var generator (SVG) is generally applied to parallel with the VSG. Firstly, the typical control strategies are given for the VSG-SVG system, and the adverse impacts of the voltage droop characteristics is investigated based on the power-angle curve. Then, a full-order nonlinear dynamic model of the VSG-SVG system is established. With the application of T-S fuzzy modeling and linear matrix inequality (LMI) methods, a Lyapunov-based stability criterion is proposed to estimate the stability region of the paralleled system. Finally, the impacts of circuit parameters and controller parameters on the system stability are studied. To validate the effectiveness of the proposed stability analysis, the MATLAB simulation and hardware-in-loop experiment are carried out.