Abstract
The article presents the results carried out within the framework of the grant project of the Ministry of Science and Higher Education of the Republic of Kazakhstan AP19675193. In this paper we study the nonlinear problem of constructing material systems whose motions are described by ordinary differential equations, and the nonlinearity of the system satisfies the condition of a locally quadratic connection. We constructed the comparison systems to study stability in the neighborhood of program manifold. Moreover, we obtained the sufficient conditions for absolute stability with respect to a given function. Methods based on mappings of the state space of the original system into the state space of auxiliary comparison systems that preserve the dynamic properties under study are widely used in solving a manifold of theoretical and applied problems. In this work, matrix comparison equations are used to obtain sufficient stability conditions for the program manifold of non-autonomous control systems and systems with scalar control.