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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 3, Pages 185–201 (Mi timm415)  
This article is cited in 22 scientific papers (total in 23 papers)

Extension of E. A. Barbashin's and N. N. Krasovskii's stability theorems to controlled dynamical systems

E. A. Panasenkoa, E. L. Tonkovb

a Tambov State University
b Udmurt State University
Full-text PDF (276 kB) Citations (23)
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Abstract: The known theorems by E. A. Barbashin and N. N. Krasovskii (1952) about the asymptotic and global stability of an equilibrium state for an autonomous system of differential equations are extended to nonautonomous differential inclusions with closed-valued (but not necessarily compact-valued) right-hand sides, where the equilibrium state is a weakly invariant (with respect to the solutions of the inclusion) set. The statements are formulated in terms of the Hausdorff–Bebutov metric, the dynamical system of translations corresponding to the right-hand side of the differential inclusion, and the weakly invariant set corresponding to the inclusion.
Keywords: stability theory, Lyapunov functions, differential inclusions, controlled systems, invariant sets.
Received: 28.02.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 268, Issue 1, Pages S204–S221
DOI: https://doi.org/10.1134/S0081543810050159
Bibliographic databases:
Document Type: Article
UDC: 517.911+517.93
Language: Russian
Citation: E. A. Panasenko, E. L. Tonkov, “Extension of E. A. Barbashin's and N. N. Krasovskii's stability theorems to controlled dynamical systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 185–201; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S204–S221
Citation in format AMSBIB
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\paper Extension of E.\,A.~Barbashin's and N.\,N.~Krasovskii's stability theorems to controlled dynamical systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 3
\pages 185--201
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\elib{https://elibrary.ru/item.asp?id=12834741}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 268
\issue , suppl. 1
\pages S204--S221
\crossref{https://doi.org/10.1134/S0081543810050159}
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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