Geodesic
A new class of Lyapunov functions for stability analysis of singular dynamical systems. Elements of $p$-regularity theory
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 8-12

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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. 
@article{DANMA_2021_499_a1,
     author = {Yu. G. Evtushenko and A. A. Tret'yakov},
     title = {A new class of {Lyapunov} functions for stability analysis of singular dynamical systems. {Elements} of $p$-regularity theory},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {8--12},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_499_a1/}
}
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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. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 8-12. http://geodesic.mathdoc.fr/item/DANMA_2021_499_a1/