Abstract: Based on both Routh stability criterion and state equation transformation with complex coefficients, the voltage build-up analysis for the self-excited induction generator（SEIG） autonomous system was realized. On the basis of the 3×3 order state equations in two phase stationary reference frame with complex coefficients, the difficulty solving process for the determinant of the SEIG characteristic equation were reduced. Moreover, the sufficient and necessary conditions of system stability with complex coefficients of Routh stability criterion were confirmed, particularly the whole critical excitation capacitance and boundary curves of the SEIG from rest to rated speed without loads were calculated and drew. The efficiency and the accuracy of SEIG voltage stability analysis were verified by the results of calculated example, simulation and experiment. According to the proposed methodology for calculating and analyzing the stability boundary of SEIG in this article, the feasibility of Routh criterion with complex coefficients for the analysis of steady voltage build-up of autonomous system was proved. The conclusion lay a foundation for further application in the stability analysis of SEIG with complex coefficients of state equation and Routh criterion.