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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 3, Pages 38–55 (Mi timm405)  
This article is cited in 13 scientific papers (total in 13 papers)

Analysis of coordinate and other transformations of models of dynamical systems by the reduction method

S. N. Vassilyeva, R. I. Kozlovb, S. A. Ul'yanova

a Institute of Control Sciences, Russian Academy of Sciences
b Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (265 kB) Citations (13)
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Abstract: The issues of preserving dynamic properties when passing from a system of differential equations to another system obtained by a change of variables are considered, as well as issues of preserving the properties in the opposite direction. The possibilities of the reduction method, which was proposed earlier, in resolving these questions are demonstrated by the examples of such properties as stability, attraction, and dissipativity. Similar questions are investigated for the case when the second system is obtained by a way characteristic for the comparison method with vector Lyapunov functions. The application of one of the obtained dissipativity criteria to analyzing the nonlinear dynamics of a group of moving objects is considered.
Keywords: differential equations, stability, dissipativity, reduction method, coordinate transformations, vector Lyapunov functions, group control, formation stability.
Received: 29.04.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 268, Issue 1, Pages S264–S282
DOI: https://doi.org/10.1134/S0081543810050184
Bibliographic databases:
Document Type: Article
UDC: 517+519
Language: Russian
Citation: S. N. Vassilyev, R. I. Kozlov, S. A. Ul'yanov, “Analysis of coordinate and other transformations of models of dynamical systems by the reduction method”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 38–55; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S264–S282
Citation in format AMSBIB
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\paper Analysis of coordinate and other transformations of models of dynamical systems by the reduction method
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 3
\pages 38--55
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S264--S282
\crossref{https://doi.org/10.1134/S0081543810050184}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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