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

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] ;  [2]
  1. Hadmark University College (Norway)
  2. Timoshenko Institute of Mathematics, NAS of Ukraine, Kiev (Ukraine)
Publication Date:
OSTI Identifier:
22365113
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; DIFFERENTIAL EQUATIONS; EQUILIBRIUM; LYAPUNOV METHOD; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILITY