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Mat. Zametki, 2011, Volume 90, Issue 6, Pages 803–820 (Mi mz6609)  

This article is cited in 2 scientific papers (total in 2 papers)

Stability Analysis Based on Nonlinear Inhomogeneous Approximation

A. Yu. Aleksandrov, A. V. Platonov

Saint-Petersburg State University

Abstract: The asymptotic stability of zero solutions for essentially nonlinear systems of differential equations in triangular inhomogeneous approximation is studied. Conditions under which perturbations do not affect the asymptotic stability of the zero solution are determined by using the direct Lyapunov method. Stability criteria are stated in the form of inequalities between perturbation orders and the orders of homogeneity of functions involved in the nonlinear approximation system under consideration.

Keywords: asymptotic stability, Lyapunov function, nonlinear approximation, cascade system, homogeneous function

DOI: https://doi.org/10.4213/mzm6609

Full text: PDF file (534 kB)
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English version:
Mathematical Notes, 2011, 90:6, 787–800

Bibliographic databases:

UDC: 517.925.51
Received: 08.12.2008
Revised: 18.11.2010

Citation: A. Yu. Aleksandrov, A. V. Platonov, “Stability Analysis Based on Nonlinear Inhomogeneous Approximation”, Mat. Zametki, 90:6 (2011), 803–820; Math. Notes, 90:6 (2011), 787–800

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Sultanbekov, “Ob ustoichivosti odnogo klassa suschestvenno nelineinykh raznostnykh sistem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(27) (2012), 132–143  mathnet  crossref  zmath
    2. Sultanbekov A.A., “Usloviya ustoichivosti odnogo klassa suschestvenno nelineinykh raznostnykh sistem”, Nauchno-tekhnicheskii vestnik Povolzhya, 2012, no. 1, 216–216  elib
  • Математические заметки Mathematical Notes
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