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Nonlinear analysis of phase-locked loop (PLL) : Global stability analysis, hidden oscillations and simulation problems. / Leonov, G. A.; Kuznetsov, N. V.

Mechanics and Model-Based Control of Advanced Engineering Systems. Springer Nature, 2014. p. 199-206.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Leonov, GA & Kuznetsov, NV 2014, Nonlinear analysis of phase-locked loop (PLL): Global stability analysis, hidden oscillations and simulation problems. in Mechanics and Model-Based Control of Advanced Engineering Systems. Springer Nature, pp. 199-206. https://doi.org/10.1007/978-3-7091-1571-8_22, https://doi.org/10.1007/978-3-7091-1571-8_22

APA

Leonov, G. A., & Kuznetsov, N. V. (2014). Nonlinear analysis of phase-locked loop (PLL): Global stability analysis, hidden oscillations and simulation problems. In Mechanics and Model-Based Control of Advanced Engineering Systems (pp. 199-206). Springer Nature. https://doi.org/10.1007/978-3-7091-1571-8_22, https://doi.org/10.1007/978-3-7091-1571-8_22

Vancouver

Leonov GA, Kuznetsov NV. Nonlinear analysis of phase-locked loop (PLL): Global stability analysis, hidden oscillations and simulation problems. In Mechanics and Model-Based Control of Advanced Engineering Systems. Springer Nature. 2014. p. 199-206 https://doi.org/10.1007/978-3-7091-1571-8_22, https://doi.org/10.1007/978-3-7091-1571-8_22

Author

Leonov, G. A. ; Kuznetsov, N. V. / Nonlinear analysis of phase-locked loop (PLL) : Global stability analysis, hidden oscillations and simulation problems. Mechanics and Model-Based Control of Advanced Engineering Systems. Springer Nature, 2014. pp. 199-206

BibTeX

@inbook{461e5806482f4685a91c8d3c952de50d,
title = "Nonlinear analysis of phase-locked loop (PLL): Global stability analysis, hidden oscillations and simulation problems",
abstract = "In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar{\textquoteright} revealed a gap in Kapranov{\textquoteright}s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model. From a computational point of view the system considered was globally stable (all the trajectories tended to equilibria), but, in fact, there was a bounded domain of attraction only. In this review, following ideas of N. Gubar{\textquoteright}, the qualitative analysis of hidden oscillation bifurcation in a two-dimensional model of phase-locked loop is considered.",
author = "Leonov, {G. A.} and Kuznetsov, {N. V.}",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Wien 2014.",
year = "2014",
month = jan,
day = "1",
doi = "10.1007/978-3-7091-1571-8_22",
language = "English",
isbn = "9783709115701",
pages = "199--206",
booktitle = "Mechanics and Model-Based Control of Advanced Engineering Systems",
publisher = "Springer Nature",
address = "Germany",

}

RIS

TY - CHAP

T1 - Nonlinear analysis of phase-locked loop (PLL)

T2 - Global stability analysis, hidden oscillations and simulation problems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

N1 - Publisher Copyright: © Springer-Verlag Wien 2014.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar’ revealed a gap in Kapranov’s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model. From a computational point of view the system considered was globally stable (all the trajectories tended to equilibria), but, in fact, there was a bounded domain of attraction only. In this review, following ideas of N. Gubar’, the qualitative analysis of hidden oscillation bifurcation in a two-dimensional model of phase-locked loop is considered.

AB - In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar’ revealed a gap in Kapranov’s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model. From a computational point of view the system considered was globally stable (all the trajectories tended to equilibria), but, in fact, there was a bounded domain of attraction only. In this review, following ideas of N. Gubar’, the qualitative analysis of hidden oscillation bifurcation in a two-dimensional model of phase-locked loop is considered.

UR - http://www.scopus.com/inward/record.url?scp=84919389162&partnerID=8YFLogxK

U2 - 10.1007/978-3-7091-1571-8_22

DO - 10.1007/978-3-7091-1571-8_22

M3 - Chapter

SN - 9783709115701

SP - 199

EP - 206

BT - Mechanics and Model-Based Control of Advanced Engineering Systems

PB - Springer Nature

ER -

ID: 4697171