In this paper, pi‐coefficients are used to represent the linear time‐invariant error subsystem and to analyze the nonlinear time‐varying update rule of the error model for a model‐reference adaptive system (MRAS). Several factors affecting the system stabilities — unmodeled dynamics, sampling intervals, input frequency, andσ‐modification — are analyzed by the quantitativer‐pcurves. By this analysis, the gradient update rule is quantitatively shown a feature lacking robustness in an MRAS, but it can be improved by utilizingσ‐modification. All these factors can easily be determined by the pi‐coefficients to obtain the best robust characteristics.