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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 2, Pages 281–289
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000351
(Mi rcd674)
 

This article is cited in 47 scientific papers (total in 47 papers)

On the 70th birthday of L.P. Shilnikov

Generalization of the Andronov–Vitt theorem

G. A. Leonov

Department of Mathematics and Mechanics, Saint Petersburg State University, 2, Bibliotechnaya pl., Petrodvoretz, 198904 Saint Petersburg, Russia
Citations (47)
Abstract: A definition of Zhukovski stability is introduced. A new research tool— a moving Poincaré section— is considered. With the help of this tool, generalizations of the Andronov–Vitt and Demidovich theorems are obtained.
Keywords: Orbital stability, Zhukovski stability, Characteristic exponent, Poincaré section.

Accepted: 01.07.2005
Bibliographic databases:
Document Type: Article
MSC: 34D20
Language: English
Citation: G. A. Leonov, “Generalization of the Andronov–Vitt theorem”, Regul. Chaotic Dyn., 11:2 (2006), 281–289
Citation in format AMSBIB
\Bibitem{Leo06}
\by G. A. Leonov
\paper Generalization of the Andronov–Vitt theorem
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 2
\pages 281--289
\mathnet{http://mi.mathnet.ru/rcd674}
\crossref{https://doi.org/10.1070/RD2006v011n02ABEH000351}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2245083}
\zmath{https://zbmath.org/?q=an:1164.34448}
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  • https://www.mathnet.ru/eng/rcd674
  • https://www.mathnet.ru/eng/rcd/v11/i2/p281
  • This publication is cited in the following 47 articles:
    1. Xuyang Lou, Yuchun Li, Ricardo G. Sanfelice, “Notions, Stability, Existence, and Robustness of Limit Cycles in Hybrid Dynamical Systems”, IEEE Trans. Automat. Contr., 69:8 (2024), 4910  crossref
    2. D.D. Bain, “Variational equation for discontinuous delayed systems”, Partial Differential Equations in Applied Mathematics, 2024, 101034  crossref
    3. Maksim O. Surov, Stepan S. Pchelkin, Anton S. Shiriaev, Sergei V. Gusev, Leonid B. Freidovich, 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024, 12679  crossref
    4. Peter Giesl, Sigurdur Hafstein, Christoph Kawan, “Review on contraction analysis and computation of contraction metrics”, JCD, 10:1 (2023), 1  crossref
    5. Eva Ahbe, Andrea Iannelli, Roy S. Smith, “A novel moving orthonormal coordinate-based approach for region of attraction analysis of limit cycles”, JCD, 10:1 (2023), 75  crossref
    6. Christian Fredrik Sætre, Anton Shiriaev, “Orbital stabilization of point-to-point maneuvers in underactuated mechanical systems”, Automatica, 147 (2023), 110735  crossref
    7. Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad, “Robustness of Numerically Computed Contraction Metrics”, SN COMPUT. SCI., 3:4 (2022)  crossref
    8. Saetre Ch.F., Shiriaev A.S., Freidovich L.B., Gusev V S., Fridman L.M., “Robust Orbital Stabilization: a Floquet Theory-Based Approach”, Int. J. Robust Nonlinear Control, 31:16 (2021), 8075–8108  crossref  mathscinet  isi  scopus
    9. Nikolay Kuznetsov, Volker Reitmann, Emergence, Complexity and Computation, 38, Attractor Dimension Estimates for Dynamical Systems: Theory and Computation, 2021, 309  crossref
    10. Alexander Zuyev, Peter Benner, Andreas Seidel-Morgenstern, “On the orbital stability of periodic trajectories of a class of discontinuous systems”, Proc Appl Math & Mech, 21:1 (2021)  crossref
    11. Herrera L., Orlov Yu., Montano O., Shiriaev A., “Model Orbit Output Feedback Tracking of Underactuated Mechanical Systems With Actuator Dynamics”, Int. J. Control, 93:2, SI (2020), 293–306  crossref  mathscinet  zmath  isi  scopus
    12. Surov M., Gusev S., Freidovich L., “Constructing Transverse Coordinates For Orbital Stabilization of Periodic Trajectories”, 2020 American Control Conference (Acc), Proceedings of the American Control Conference, IEEE, 2020, 836–841  crossref  isi
    13. Saetre Ch.F., Shiriaev A., Pchelkin S., Chemori A., “Excessive Transverse Coordinates For Orbital Stabilization of (Underactuated) Mechanical Systems”, 2020 European Control Conference (Ecc 2020), IEEE, 2020, 895–900  crossref  isi
    14. Christian Fredrik Sætre, Anton Shiriaev, “On excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions”, IFAC-PapersOnLine, 53:2 (2020), 9250  crossref
    15. Sh. Mamedov, R. Khusainov, S. Gusev, A. Klimchik, A. Maloletov, A. Shiriaev, “Underactuated mechanical systems: Whether orbital stabilization is an adequate assignment for a controller design?”, IFAC-PapersOnLine, 53:2 (2020), 9262  crossref
    16. Shiryaev A.S., Khusainov R.R., Mamedov Sh.N., Gusev S.V., Kuznetsov N.V., “On Leonov'S Method For Computing the Linearization of Transverse Dynamics and Analyzing Zhukovsky Stability”, Vestn. St Petersb. Univ.-Math., 52:4 (2019), 334–341  crossref  mathscinet  isi  scopus
    17. Saetre Ch.F., Shiriaev A., Anstensrud T., “Trajectory Optimization and Orbital Stabilization of Underactuated Euler-Lagrange Systems With Impacts”, 2019 18Th European Control Conference (Ecc), IEEE, 2019, 758–763  isi
    18. Christian Fredrik Saetre, Anton Shiriaev, Torleif Anstensrud, 2019 18th European Control Conference (ECC), 2019, 758  crossref
    19. Venus Pasandi, Aiko Dinale, Mehdi Keshmiri, Daniele Pucci, 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, 8007  crossref
    20. Alireza Mohammadi, Manfredi Maggiore, Luca Consolini, “Dynamic virtual holonomic constraints for stabilization of closed orbits in underactuated mechanical systems”, Automatica, 94 (2018), 112  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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