To investigate the error convergence characteristics of power battery polarization parameter estimation under different operating conditions， the stability and convergence of the estimators are rigorously analyzed in this paper by using Lyapunov’s second method. The state equations of polarized parameter estimation errors are firstly derived based on the equivalent circuit model and the forgetting factor recursive least squares （FFRLS）. Subsequently， the state equation is analyzed using Lyapunov’s second method to obtain the necessary condition for the asymptotic convergence of the estimator， i.e.， continuously varying current input. A graphical method is proposed for analyzing the dynamic convergence properties of the error and justifying this necessary condition. Finally， the theoretical analysis process and results are validated using data generated from an experimentally calibrated battery model. The results show that the estimator can gradually converge to the vicinity of the true value under continuously varying current inputs， and the drastically varying positive and negative alternating conditions have better convergence properties.