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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 6, Pages 1215–1233
DOI: https://doi.org/10.17377/smzh.2015.56.602 (Mi smj2708) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Analysis of stability and stabilization of nonlinear systems via decomposition

A. Yu. Aleksandrova, A. P. Zhabkoa, A. A. Kosovb

a St. Petersburg State University, St. Petersburg, Russia
b Institute for System Dynamics and Control Theory, Irkutsk, Russia
Full-text PDF (350 kB) Citations (8)
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DOI: https://doi.org/10.17377/smzh.2015.56.602
Abstract: We establish necessary and sufficient conditions for the solvability of a Lyapunov-type system of PDEs in the class of homogeneous functions. Using these, we propose an approach to studying the stability of an equilibrium of an essentially nonlinear system of ODEs in the critical case of $n$ zero roots and $n$ pure imaginary roots. The approach bases on decomposition of the system in question into two separate subsystems of half dimension.
Keywords: Lyapunov system, homogeneous solution, nonlinear system, decomposition, asymptotic stability, stabilization.
Received: 01.03.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 6, Pages 968–981
DOI: https://doi.org/10.1134/S0037446615060026
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
Language: Russian
Citation: A. Yu. Aleksandrov, A. P. Zhabko, A. A. Kosov, “Analysis of stability and stabilization of nonlinear systems via decomposition”, Sibirsk. Mat. Zh., 56:6 (2015), 1215–1233; Siberian Math. J., 56:6 (2015), 968–981
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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