As one of the converter family based on modular multilevel converters technology, the modular multilevel matrix converter (M3C) is a promising grid-connected converter topology for large-scale renewable energy transmission in low-frequency ac/ac system and upgrading power transmission capacity of urban network. But the existing methods of small-signal stability of M3C are inapplicable for analysis under large-signal power fluctuation conditions. Consequently, this study comprehensively performs a large-signal stability analysis of M3C under power fluctuation, considering the sophisticated inner and outer loop decoupling control strategy, subconverter voltage balancing approach, and different-frequency interaction factor. Based on Takagi–Sugeno fuzzy model theory, the Lyapunov function is constructed and the corresponding large-signal stability domain of attraction (LS-DOA) is obtained efficiently. Furthermore, the stability strength by synthesizing the minimum energy boundaries and rotating angles of LS-DOA is proposed as a quantitative index to improve the traditional qualitative observation method. By taking into account the different-frequency interaction factor, it further proposes the enhancement methods for the large-signal stability from two aspects: topology structural parameters optimization and control strategy improvement. Ultimately, the effectiveness of the proposed method is verified through simulation and experimental results.