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A New Class of Lyapunov Functions for Stability Analysis of Singular Dynamical Systems. Elements of p -Regularity Theory

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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.

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Funding

This study was supported by the Russian Science Foundation, project no. 21-71-30005.

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Authors and Affiliations

  1. Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 119333, Moscow, Russia

    Yu. G. Evtushenko & A. A. Tret’yakov

  2. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    Yu. G. Evtushenko

  3. System Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    A. A. Tret’yakov

  4. Faculty of Sciences, Siedlce University of Natural Sciences and Humanities, 08-110, Siedlce, Poland

    A. A. Tret’yakov

Authors
  1. Yu. G. Evtushenko
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  2. A. A. Tret’yakov
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Corresponding authors

Correspondence to Yu. G. Evtushenko or A. A. Tret’yakov.

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Translated by N. Berestova

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Evtushenko, Y.G., Tret’yakov, A.A. A New Class of Lyapunov Functions for Stability Analysis of Singular Dynamical Systems. Elements of p -Regularity Theory . Dokl. Math. 104, 165–168 (2021). https://doi.org/10.1134/S1064562421040062

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  • DOI: https://doi.org/10.1134/S1064562421040062

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