Abstract: When grid-following converters (GFLC) are connected in parallel with grid-forming converters (GFMC) for grid-connected power supply, the tracking of maximum new energy output can be achieved, and frequency and voltage support can be provided. However, they also suffer from transient instability under large disturbances. This study employs the Takagi-Sugeno (TS) fuzzy model and linear matrix inequality techniques to quantitatively assess the influence of parameters on transient stability in a power supply system with GFLC paralleled with GFMC. Firstly, based on the topology and control strategy of the power supply system with GFLC paralleled with GFMC, a nonlinear model is established and converted into a TS fuzzy model. Secondly, a Lyapunov function (LF) is constructed to estimate the domain of attraction of the system by solving the LMI. On this basis, the impact of various system parameters and the parallel connection of GFMC and GFLC on system stability is analyzed, providing theoretical support for enhancing system transient stability through system parameter optimization. Finally, the correctness of the stability analysis is verified through MATLAB simulations and a hardware-in-loop experiment.