Geodesic
Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action
Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 862-891

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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: quasihomogeneous system, Lyapunov stability, Lyapunov's direct method.
Mots-clés : impulsive action 
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     author = {A. I. Dvirnyj and V. I. Slyn'ko},
     title = {Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action},
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A. I. Dvirnyj; V. I. Slyn'ko. Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action. Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 862-891. http://geodesic.mathdoc.fr/item/SM_2014_205_6_a4/