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Matematicheskie Zametki, 2011, Volume 90, Issue 6, Pages 803–820
DOI: https://doi.org/10.4213/mzm6609 (Mi mzm6609) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Stability Analysis Based on Nonlinear Inhomogeneous Approximation

A. Yu. Aleksandrov, A. V. Platonov

Saint-Petersburg State University
Full-text PDF (534 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm6609
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.
Received: 08.12.2008
Revised: 18.11.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 6, Pages 787–800
DOI: https://doi.org/10.1134/S0001434611110198
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
Language: Russian
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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  • https://doi.org/10.4213/mzm6609
  • https://www.mathnet.ru/eng/mzm/v90/i6/p803
    • This publication is cited in the following 3 articles:
    1. Gökhan Şahan, “Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms”, Journal of the Franklin Institute, 360:13 (2023), 10275  crossref
    2. 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
    3. Sultanbekov A.A., “Usloviya ustoichivosti odnogo klassa suschestvenno nelineinykh raznostnykh sistem”, Nauchno-tekhnicheskii vestnik Povolzhya, 2012, no. 1, 216–216  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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