On the stability of singular homogeneous systems

Title	On the stability of singular homogeneous systems
Authors	A. A. Kosov¹, M. V. Kozlov² ¹Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences ²National Research Ogarev Mordovia State University
Annotation	We consider singularly perturbed systems of ordinary differential equations whose right-hand side contains homogeneous first-order functions. The research results are sufficient conditions under which the properties of asymptotic stability and instability of the zero solution of the original system is a consequence of the analogous property of the zero solution of the systems of fast and slow motions obtained as a result of decomposition of the initial system.
Keywords	singular systems, homogeneous functions, stability, decomposition
Citation	Kosov A. A., Kozlov M. V. ''On the stability of singular homogeneous systems'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 360-363. Available at: https://conf.svmo.ru/files/deamm2017/papers/paper50.pdf. - Date of access: 04.12.2024.