Digital implementation of control systems made it possible to improve the quality and reliability of power supply through more sophisticated algorithms for regulating the excitation of synchronous generators. A promising direction of development of automatic excitation control systems is the development of adaptive system stabilizers for effective damping of electromechanical oscillations in power systems. One of the options for solving the problem of adaptive control is to adjust the system stabilizer with the help of a fuzzy approximator. The fuzzy approximator, depending on the parameters of the power system, determines the optimum coefficients of the stabilization channels for excess power and the speed deviation of the power unit. It is especially important to ensure the optimum tuning of the system stabilizer in the under-excitation mode. The article shows that the regularities connecting the optimum coefficients of the automatic voltage regulator and the system stabilizer with the parameters of the power system selected in normal generator modes are also valid for the under-excitation mode.