Application of algebraic-geometric properties of linear systems of differential equations to the study of partial stability

Title	Application of algebraic-geometric properties of linear systems of differential equations to the study of partial stability
Authors	V. I. Nikonov¹ ¹National Research Mordovia State University
Annotation	Partial stability of linear systems of differential equations with constant coefficients is investigated. Using the algebraic and geometric properties of the sum of cyclic subspaces of a linear operator that partially determines the dynamics of the system, stability conditions with respect to a given part of the coordinates of the phase vector are obtained. The existence of an invariant subspace of a linear operator allows us to reduce the problem of partial stability to the analysis of the stability of a selected subsystem.
Keywords	linear operator, cyclic subspace, minimal annihilating polynomial, partial stability.
Citation	Nikonov V. I. ''Application of algebraic-geometric properties of linear systems of differential equations to the study of partial stability'' [Electronic resource]. Proceedings of the XVII International scientific conference "Differential equations and their applications in mathematical modeling". Saransk: SVMO Publ, 2025. - pp. 206-211. Available at: https://conf.svmo.ru/files/2025/papers/paper41.pdf. - Date of access: 18.10.2025.