Applied Physics and Mathematics Annotation << Back DETERMINATION OF STABLE EQUILIBRIUM STATE AT CONTROL OF DYNAMIC OBJECT BY CONSTRUCTING HOMOTOPY OPERATOR S.N. CHUKANOV The geometric methods of determining the stability of the equilibrium state of dynamical systems at critical points is proposes in the paper. Method is extended on dynamic control system objects determined by a system of diff erential equations of the fi rst order. Formation of control signals of control system causes to a change in the geometric characteristics of the system that allows transfer the system from a state of unstable equilibrium to a state of stable equilibrium. Stable equilibrium is determined by the method of determining the index non-degenerate critical point of the Morse function, which is used as the potential function of a dynamic system. Keywords: control system of dynamic object, stability of equilibrium state of dynamic system, Morse function, operator homotopy, theorem Jacobi. Contacts: E-mail: gromovtambov@yandex.ru Pp. 46-50.