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Avtomat. i Telemekh., 2006, Issue 10, Pages 47–85 (Mi at1245)  

This article is cited in 40 scientific papers (total in 40 papers)

Phase synchronization: Theory and applications

G. A. Leonov

St. Petersburg State University

Abstract: The state-of-the-art of the phase synchronization theory was reviewed. Consideration was given to its applications to the synchronous and induction electrical motors, phase locked loops, and autosynchronization of the unbalanced rotors. The Yakubovich–Kalman frequency theorem was widely used to study the phase synchronization systems for global stability.

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English version:
Automation and Remote Control, 2006, 67:10, 1573–1609

Bibliographic databases:

PACS: 02.30.Yy, 01.60.+q
Presented by the member of Editorial Board: Б. Т. Поляк

Received: 07.02.2006

Citation: G. A. Leonov, “Phase synchronization: Theory and applications”, Avtomat. i Telemekh., 2006, no. 10, 47–85; Autom. Remote Control, 67:10 (2006), 1573–1609

Citation in format AMSBIB
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\by G.~A.~Leonov
\paper Phase synchronization: Theory and applications
\jour Avtomat. i Telemekh.
\yr 2006
\issue 10
\pages 47--85
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2268317}
\zmath{https://zbmath.org/?q=an:1195.37016}
\transl
\jour Autom. Remote Control
\yr 2006
\vol 67
\issue 10
\pages 1573--1609
\crossref{https://doi.org/10.1134/S0005117906100031}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750195767}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. R. Liberzon, “Essays on the absolute stability theory”, Autom. Remote Control, 67:10 (2006), 1610–1644  mathnet  crossref  mathscinet  zmath  elib  elib
    2. G. A. Leonov, “Mathematical models of phase syncronization systems with quadrature and phase-quadrature units”, Autom. Remote Control, 69:9 (2008), 1475–1485  mathnet  crossref  mathscinet  zmath  isi
    3. Leonov G.A., “The passage through resonance of synchronous electric motors mounted on an elastic base”, J Appl Math Mech, 72:6 (2008), 631–637  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Leonov G.A., “Computation of phase detector characteristics in phase locked loops for clock synchronization”, Doklady Mathematics, 78:1 (2008), 643–645  crossref  mathscinet  isi  elib  scopus
    5. G. A. Leonov, “Analysis and synthesis of controlled delay lines”, Autom. Remote Control, 70:10 (2009), 1760–1766  mathnet  crossref  mathscinet  zmath  isi
    6. Altenbach H., Brigadnov I.A., Naumenko K., “Rotation of a slender particle in a shear flow: influence of the rotary inertia and stability analysis”, ZAMM Z Angew Math Mech, 89:10 (2009), 823–832  crossref  mathscinet  zmath  isi  elib  scopus
    7. Leonov G.A., “Analysis and synthesis of controlled delay lines for fast digital devices”, Doklady Mathematics, 80:1 (2009), 633–636  crossref  mathscinet  isi  elib  scopus
    8. Kuznetsov N.V., Leonov G.A., Seledzhi S.M., Neittaanmaki P., “Analysis and Design of Computer Architecture Circuits with Controllable Delay Line”, ICINCO 2009: Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics, 2009, 221–224  mathscinet  isi
    9. Perkin A., Smirnova V., Shepeljavyi A., “Frequency-domain criteria for gradient-like behavior of phase control systems with vector nonlinearities”, 2009 IEEE Control Applications CCA & Intelligent Control (ISIC), IEEE International Conference on Control Applications, 2009, 142–146  isi
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    11. Leonov G.A., Fyodorov A.A., “Frequency Oscillations Estimates for Digital Phase-Locked Loops”, Doklady Mathematics, 84:2 (2011), 761–764  crossref  mathscinet  zmath  isi  elib  elib  scopus
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    13. Ugrinovskii V., Langbort C., “Distributed H-infinity consensus-based estimation of uncertain systems via dissipativity theory”, Iet Control Theory and Applications, 5:12 (2011), 1458–1469  crossref  mathscinet  isi  scopus
    14. Perkin A.A., Smirnova V.B., Utina N.V., Shepelyavyi A.I., “O primenenii metoda periodicheskikh funktsii lyapunova”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: Matematika. Mekhanika. Astronomiya, 2011, no. 3, 36–47  mathscinet  zmath  elib
    15. Hua Ouyang, Petersen I.R., Ugrinovskii V., “Lagrange Stabilization of Pendulum-Like Systems: A Pseudo H-infinity Control Approach”, IEEE Trans Automat Control, 57:3 (2012), 649–662  crossref  mathscinet  zmath  isi  scopus
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    17. Ouyang H., Petersen I.R., Ugrinovskii V., “Stability Analysis and State Feedback Stabilization of Pendulum-Like Systems with Multiple Nonlinearities”, Automatica, 48:9 (2012), 2235–2243  crossref  mathscinet  zmath  isi  elib  scopus
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    22. Popov S.A., “Method of Positively Invariant Cones For Evolution Systems With Cubic and Periodic Nonlinearities”, Differ. Equ., 50:13 (2014), 1739–1751  crossref  mathscinet  zmath  isi  scopus
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    25. Leonov G.A., Kuznetsov N.V., Yuldahsev M.V., Yuldashev R.V., “Computation of the Phase Detector Characteristic of Classical Pll”, Dokl. Math., 91:2 (2015), 246–249  crossref  mathscinet  zmath  isi  elib  scopus
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