On the stability of singular homogeneous systems

TitleOn the stability of singular homogeneous systems
AuthorsA. 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
AnnotationWe 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.
Keywordssingular systems, homogeneous functions, stability, decomposition
CitationKosov 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: http://conf.svmo.ru/files/deamm2017/papers/paper50.pdf. - Date of access: 24.06.2019.