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

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. (paper)

Authors:
 [1]
  1. Hadmark University College (Norway)
Publication Date:
OSTI Identifier:
22365113
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 205; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; DIFFERENTIAL EQUATIONS; EQUILIBRIUM; LYAPUNOV METHOD; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILITY

Citation Formats

Dvirny, A. I., and Slyn'ko, V. I., E-mail: dvirny@mail.ru, E-mail: vitstab@ukr.net. Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N06ABEH004401.
Dvirny, A. I., & Slyn'ko, V. I., E-mail: dvirny@mail.ru, E-mail: vitstab@ukr.net. Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action. United States. https://doi.org/10.1070/SM2014V205N06ABEH004401
Dvirny, A. I., and Slyn'ko, V. I., E-mail: dvirny@mail.ru, E-mail: vitstab@ukr.net. 2014. "Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action". United States. https://doi.org/10.1070/SM2014V205N06ABEH004401.
@article{osti_22365113,
title = {Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action},
author = {Dvirny, A. I. and Slyn'ko, V. I., E-mail: dvirny@mail.ru, E-mail: vitstab@ukr.net},
abstractNote = {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. (paper)},
doi = {10.1070/SM2014V205N06ABEH004401},
url = {https://www.osti.gov/biblio/22365113}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 6,
volume = 205,
place = {United States},
year = {Sun Jun 01 00:00:00 EDT 2014},
month = {Sun Jun 01 00:00:00 EDT 2014}
}