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Extended Abstracts Spring 2018 pp 245–251Cite as

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Stabilization of Unstable Periodic Solutions for Inverted Pendulum Under Hysteretic Control: The Magnitskii Approach

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Part of the book series: Trends in Mathematics ((RPCRMB,volume 11))

Abstract

In this paper, a mathematical model of the stabilization of the inverted pendulum with vertically oscillating suspension under hysteretic control is constructed. The stabilization of unstable periodic solutions for such a system is considered using the Magnitskii approach.

This work was supported by the RFBR (Grants 16-08-00312-a, 17-01-00251-a, 18-47-310003 and 18-08-00053-a).

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Author information

Authors and Affiliations

  1. Voronezh State University, Universitetskaya sq.1, 394006, Voronezh, Russia

    Mikhail E. Semenov & Peter A. Meleshenko

  2. Geophysical Survey of Russia Academy of Science, Lenina av. 189, 249035, Obninsk, Russia

    Mikhail E. Semenov

  3. Voronezh State Technical University, XX-letiya Oktyabrya st. 84, 394006, Voronezh, Russia

    Mikhail E. Semenov & Zainib Hatif Abbas

  4. Zhukovsky–Gagarin Air Force Academy, Starykh Bolshevikov st. 54 “A”, 394064, Voronezh, Russia

    Mikhail E. Semenov, Peter A. Meleshenko & Igor N. Ishchuk

  5. Siberian Federal University, Svobodny 79, 660041, Krasnoyarsk, Russia

    Igor N. Ishchuk & Valeriy N. Tyapkin

Authors
  1. Mikhail E. Semenov
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  2. Peter A. Meleshenko
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  3. Igor N. Ishchuk
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  4. Valeriy N. Tyapkin
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  5. Zainib Hatif Abbas
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Corresponding author

Correspondence to Mikhail E. Semenov .

Editor information

Editors and Affiliations

  1. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Andrei Korobeinikov

  2. Facultat de Ciències, Universitat Autònoma de Barcelona, Barcelona, Spain

    Magdalena Caubergh

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Tomás Lázaro

  4. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Josep Sardanyés

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Semenov, M.E., Meleshenko, P.A., Ishchuk, I.N., Tyapkin, V.N., Abbas, Z.H. (2019). Stabilization of Unstable Periodic Solutions for Inverted Pendulum Under Hysteretic Control: The Magnitskii Approach. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_36

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