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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 496–503
DOI: https://doi.org/10.4213/mzm10326
(Mi mzm10326)
 

This article is cited in 15 scientific papers (total in 15 papers)

Stability in Part of the Variables of “Partial” Equilibria of Systems with Aftereffect

V. I. Vorotnikovab, Yu. G. Martyshenkoab

a Nizhny Tagil Technological Institute (branch) of Ural State Technical University
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
References:
Abstract: The problem of stability in part of the variables of a “partial” equilibrium (this means that a given part of the phase vector coordinates is zero) is considered for nonlinear nonstationary systems of functional differential equations with aftereffect. The notions of stability in part of the variables, which admit more general (compared with the known ones) assumptions about the values of the supremum-norm of the components of the initial vector function corresponding to the variables that do not determine the given equilibrium, are introduced. The stability and asymptotic stability conditions of the the type mentioned above are obtained in the context of the method of Lyapunov–Krasovskii functionals; this conditions allow generalization of several well-known results.
Keywords: stability in part of the variables, “partial” equilibrium, functional differential equations with aftereffect.
Received: 11.04.2013
Revised: 13.02.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 477–483
DOI: https://doi.org/10.1134/S0001434614090223
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. I. Vorotnikov, Yu. G. Martyshenko, “Stability in Part of the Variables of “Partial” Equilibria of Systems with Aftereffect”, Mat. Zametki, 96:4 (2014), 496–503; Math. Notes, 96:4 (2014), 477–483
Citation in format AMSBIB
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  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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