Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 499, Pages 8–12
DOI: https://doi.org/10.31857/S2686954321040068 (Mi danma182) 		 
MATHEMATICS

A new class of Lyapunov functions for stability analysis of singular dynamical systems. Elements of $p$-regularity theory

Yu. G. Evtushenkoab, A. A. Tret'yakovacd

a Dorodnitsyn Computing Centre, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
c System Research Institute, Polish Academy of Sciences, Warsaw, Poland
d Siedlce University, Faculty of Sciences, Siedlce, Poland
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DOI: https://doi.org/10.31857/S2686954321040068
Abstract: A new approach is proposed for studying the stability of dynamical systems in the case when traditional Lyapunov functions are ineffective or not applicable for research at all. The main tool used to analyze degenerate systems is the so-called $p$-factor Lyapunov function, which makes it possible to reduce the original problem to a new one based on constructions of $p$-regularity theory. An example of a meaningful application of the considered method is given.
Keywords: dynamical systems, stability, degeneration, singularity, $p$-factor Lyapunov function.
Funding agency Grant number
Russian Science Foundation 21-71-30005
This study was supported by the Russian Science Foundation, project no. 21-71-30005.
Received: 22.04.2021
Revised: 22.04.2021
Accepted: 22.04.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 1, Pages 165–168
DOI: https://doi.org/10.1134/S1064562421040062
Bibliographic databases:
Document Type: Article
UDC: 519.615
Language: Russian
Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “A new class of Lyapunov functions for stability analysis of singular dynamical systems. Elements of $p$-regularity theory”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 8–12; Dokl. Math., 104:1 (2021), 165–168
Citation in format AMSBIB
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\paper A new class of Lyapunov functions for stability analysis of singular dynamical systems. Elements of $p$-regularity theory
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\pages 8--12
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\jour Dokl. Math.
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\pages 165--168
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