This paper presents an approach to stabilizing a multidimensional nonlinear control system that is subject to a wide range of disturbances. The system is stabilized within an area with highly nonlinear effects, where control based on a linearized approximation of the system cannot provide the required level of stability. The presented approach allows for the estimation and optimization of the quality of stabilization of a nonlinear control object perturbed by a set of initial and external disturbances.