The results of the research conducted within the framework of the grant project MSHE RK AP23488811 are presented. The article examines the stability of program manifold within the main control system. To investigate the stability properties of the control system, a comparison system has been constructed. A Lyapunov function is formulated for both autonomous and non-autonomous systems. Sufficient conditions for the absolute and asymptotic stability of the program manifold are derived with respect to a function defined by the Lyapunov function. The spatial positioning of auxiliary cartographic systems is based on their representation within a given system space. These methods address various theoretical and applied problems and are also widely used for studying the dynamic properties of multi-image representations in space. Differential equations are employed to analyze comparison systems. The reduction of the order of the considered system of equations demonstrates the principal advantage of the comparison method. The stability of diverse program manifold components within automatic control systems is investigated. From the matrix comparison equations, sufficient conditions for the stability of program manifolds are obtained. Sufficient conditions for the stability of the program manifold are derived from the matrix comparison equations. Sufficient conditions for the stability of the program manifold are derived from the matrix comparison equations.