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The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges. / Кузнецов, Николай Владимирович; Лобачев, Михаил Юрьевич; Кудряшова, Елена Владимировна; Кузнецова, Ольга Александровна; Арсеньев, Дмитрий Германович.

In: Nonlinear Dynamics, Vol. 113, No. 11, 01.06.2025, p. 13771–13789.

Research output: Contribution to journal › Article › peer-review

Harvard

Кузнецов, НВ, Лобачев, МЮ, Кудряшова, ЕВ, Кузнецова, ОА & Арсеньев, ДГ 2025, 'The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges', Nonlinear Dynamics, vol. 113, no. 11, pp. 13771–13789. https://doi.org/10.1007/s11071-025-11040-3

APA

Кузнецов, Н. В., Лобачев, М. Ю., Кудряшова, Е. В., Кузнецова, О. А., & Арсеньев, Д. Г. (2025). The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges. Nonlinear Dynamics, 113(11), 13771–13789. https://doi.org/10.1007/s11071-025-11040-3

Vancouver

Кузнецов НВ, Лобачев МЮ, Кудряшова ЕВ, Кузнецова ОА, Арсеньев ДГ. The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges. Nonlinear Dynamics. 2025 Jun 1;113(11):13771–13789. https://doi.org/10.1007/s11071-025-11040-3

Author

Кузнецов, Николай Владимирович ; Лобачев, Михаил Юрьевич ; Кудряшова, Елена Владимировна ; Кузнецова, Ольга Александровна ; Арсеньев, Дмитрий Германович. / The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges. In: Nonlinear Dynamics. 2025 ; Vol. 113, No. 11. pp. 13771–13789.

BibTeX

@article{4b1606a5874f47f78b2836d0c27bc783,
title = "The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges",
abstract = "In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.",
keywords = "Global stability, Hold-in range, Lock-in range, Lyapunov functions, Nonlinear analysis, Nonlinear control systems, PLL, Phase-locked loops, Pull-in range, Viterbi problem",
author = "Кузнецов, {Николай Владимирович} and Лобачев, {Михаил Юрьевич} and Кудряшова, {Елена Владимировна} and Кузнецова, {Ольга Александровна} and Арсеньев, {Дмитрий Германович}",
year = "2025",
month = jun,
day = "1",
doi = "10.1007/s11071-025-11040-3",
language = "English",
volume = "113",
pages = "13771–13789",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Nature",
number = "11",

}

RIS

TY - JOUR

T1 - The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges

AU - Кузнецов, Николай Владимирович

AU - Лобачев, Михаил Юрьевич

AU - Кудряшова, Елена Владимировна

AU - Кузнецова, Ольга Александровна

AU - Арсеньев, Дмитрий Германович

PY - 2025/6/1

Y1 - 2025/6/1

N2 - In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.

AB - In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.

KW - Global stability

KW - Hold-in range

KW - Lock-in range

KW - Lyapunov functions

KW - Nonlinear analysis

KW - Nonlinear control systems

KW - PLL

KW - Phase-locked loops

KW - Pull-in range

KW - Viterbi problem

UR - https://www.mendeley.com/catalogue/f624d1c6-5846-3fc9-9a99-a826c409ced3/

U2 - 10.1007/s11071-025-11040-3

DO - 10.1007/s11071-025-11040-3

M3 - Article

VL - 113

SP - 13771

EP - 13789

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 11

ER -

ID: 134635821