ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 34H15

Stabilization of singularly perturbed systems with a polynomial right-hand side

M. V. Kozlov1

AnnotationThe article considers the problem stabilization of singularly perturbed systems of ordinary differential equations with homogeneous right-hand side in the form of polynomials of odd degree for sufficiently small values of the perturbing parameter. Sufficient conditions for stabilizing the zero solution of these systems to asymptotic stability by feedback control in the form of polynomials of the same degree as the right-hand side of the original system are obtained. It is assumed that only components of the vector of slow variables are subject to measurement and control can only enter into the slow subsystem. For various cases, methods for constructing stabilizing controls are described. As a method of investigation, decomposition of a singularly perturbed system into a fast and slow subsystem of smaller dimension is applied. For stability analysis, the Lyapunov function method is used.
Keywordssingular perturbations, small parameter, stabilization

1Mikhail V. Kozlov, Lecture, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), ORCID:,

Citation: M. V. Kozlov, "[Stabilization of singularly perturbed systems with a polynomial right-hand side]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 51–59 (In Russian)

DOI 10.15507/2079-6900.19.2017.01.51-59