Abstract
One of the most promising ways to solve the problem of control in the conditions of uncertainty of the characteristics of the control object and external influences is the use of adaptation methods. The article proposes to investigate the asymptotic robust stability of the reference model with the desired dynamics, using the gradient-velocity method of the Lyapunov vector-function. Considering control systems as gradient systems, and Lyapunov functions as potential functions allowed us to develop a universal gradient-velocity method of the Lyapunov vector-function, which allows to investigate the aperiodic robust stability of the reference model by the desired dynamics.