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Tr. Mat. Inst. Steklova, 2010, Volume 268, Pages 231–251 (Mi tm2865)  

This article is cited in 2 scientific papers (total in 2 papers)

Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances

Yuri S. Ledyaeva, Richard B. Vinterb

a Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA
b Department of Electrical and Electronic Engineering, Imperial College London, London, UK

Abstract: We consider a nonlinear control system which, under persistently acting disturbances, can be asymptotically driven to the origin by some non-anticipating strategy with infinite memory (such a strategy determines a value of control $u(t)$ at moment $t$ using complete information on the prehistory of disturbances until moment $t$). We demonstrate that this property is equivalent to the existence of a robust stabilizing (possibly discontinuous) feedback $k(x)$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 268, 222–241

Bibliographic databases:

Document Type: Article
UDC: 517.977.1
Received in January 2009

Citation: Yuri S. Ledyaev, Richard B. Vinter, “Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 231–251; Proc. Steklov Inst. Math., 268 (2010), 222–241

Citation in format AMSBIB
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\by Yuri~S.~Ledyaev, Richard~B.~Vinter
\paper Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 268
\pages 231--251
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm2865}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2724344}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 268
\pages 222--241
\crossref{https://doi.org/10.1134/S0081543810010153}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952255820}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Clarke F., “Lyapunov functions and discontinuous stabilizing feedback”, Annual Reviews in Control, 35:1 (2011), 13–33  crossref  isi  scopus
    2. Ledyaev Yu.S., “Program-Predictive Feedback Control For Systems With Evolving Dynamics”, IFAC PAPERSONLINE, 51:32 (2018), 723–726  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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