[Objective] In the simulation of grid-forming multi-converter systems, traditional LC equivalent model exhibits insufficient accuracy and significant transient response errors, rendering them struggle to accommodate high-frequency switching characteristics, particularly failing to accurately represent switching transient processes at sub-microsecond simulation time step. To resolve the above challenges, a high-precision modeling method for grid-forming multi-converter system based on state matrix is proposed. [Methods] Firstly, a discretized model for converter switching components under grid-forming virtual synchronous generator control was established, where undetermined parameters were determined by combining discrete circuit with ideal switching characteristic, thereby constructing a generalized fixed-admittance switching (FAS) model based on LC equivalent circuits. Secondly, based on the coupling characteristics of grid-forming multi-converter, an extension method from the single converter state matrix to the multi-converter system was derived, and system-level state-space equations were formulated to efficiently characterize dynamic interactions among converters. Finally, a grid-forming multi-converter system simulation model was established based on the PSCAD/EMTDC platform, and compared the proposed FAS model with the PSCAD ideal model and traditional LC equivalent model. [Results] The simulation results showed that the simulation results of proposed FAS model were closer to the PSCAD ideal model, which effectively reduced the power loss under the sub-microsecond simulation time step and improved the system simulation accuracy and efficiency while maintaining the system stability. [Conclusion] The proposed FAS model exhibits excellent applicability and stability under sub-microsecond simulation time step.