This article is cited in 7 papers

Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action

A. I. Dvirnyj^a, V. I. Slyn'ko<sup>b

a</sup> Hedmark University College
^b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine

Abstract: Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems.
Bibliography: 30 titles.

Keywords: impulsive action, quasihomogeneous system, Lyapunov stability, Lyapunov's direct method.

UDC: 517.925.51

MSC: Primary 35R12; Secondary 34A37

Received: 24.03.2013 and 09.12.2013

DOI: 10.4213/sm8233

 English version: Sbornik: Mathematics, 2014, 205:6, 862–891

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