Standard

Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function. / Smirnova, V. B.; Utina, N. V.; Shepelyavyi, A. I.; Perkin, A. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 42, No. 1, 01.03.2009, p. 28-36.

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

Harvard

Smirnova, VB, Utina, NV, Shepelyavyi, AI & Perkin, AA 2009, 'Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function', Vestnik St. Petersburg University: Mathematics, vol. 42, no. 1, pp. 28-36. https://doi.org/10.3103/S1063454109010051

APA

Smirnova, V. B., Utina, N. V., Shepelyavyi, A. I., & Perkin, A. A. (2009). Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function. Vestnik St. Petersburg University: Mathematics, 42(1), 28-36. https://doi.org/10.3103/S1063454109010051

Vancouver

Smirnova VB, Utina NV, Shepelyavyi AI, Perkin AA. Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function. Vestnik St. Petersburg University: Mathematics. 2009 Mar 1;42(1):28-36. https://doi.org/10.3103/S1063454109010051

Author

Smirnova, V. B. ; Utina, N. V. ; Shepelyavyi, A. I. ; Perkin, A. A. / Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function. In: Vestnik St. Petersburg University: Mathematics. 2009 ; Vol. 42, No. 1. pp. 28-36.

BibTeX

@article{a5512c4523fc4f208c83a3326a19159f,
title = "Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function",
abstract = "Two classes of phase control systems with vector nonlinearities are considered: systems described by ordinary differential equations and system described by difference equations. They are characterized by the presence of a periodic vector nonlinearity in the mathematical description of the system. The problem of the number of cycle slippings is investigated. For both classes of control systems, frequency estimates of the deviation of each angular coordinate from its initial value are obtained. The estimation technique is based on the direct Lyapunov method with periodic Lyapunov functions. With the use of the Yakubovich-Kalman lemma, all results are formulated in terms of the transfer function of the linear part of the system. The results obtained have the form of frequency inequalities with variable parameters, which satisfy some algebraic inequalities.",
author = "Smirnova, {V. B.} and Utina, {N. V.} and Shepelyavyi, {A. I.} and Perkin, {A. A.}",
year = "2009",
month = mar,
day = "1",
doi = "10.3103/S1063454109010051",
language = "English",
volume = "42",
pages = "28--36",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function

AU - Smirnova, V. B.

AU - Utina, N. V.

AU - Shepelyavyi, A. I.

AU - Perkin, A. A.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - Two classes of phase control systems with vector nonlinearities are considered: systems described by ordinary differential equations and system described by difference equations. They are characterized by the presence of a periodic vector nonlinearity in the mathematical description of the system. The problem of the number of cycle slippings is investigated. For both classes of control systems, frequency estimates of the deviation of each angular coordinate from its initial value are obtained. The estimation technique is based on the direct Lyapunov method with periodic Lyapunov functions. With the use of the Yakubovich-Kalman lemma, all results are formulated in terms of the transfer function of the linear part of the system. The results obtained have the form of frequency inequalities with variable parameters, which satisfy some algebraic inequalities.

AB - Two classes of phase control systems with vector nonlinearities are considered: systems described by ordinary differential equations and system described by difference equations. They are characterized by the presence of a periodic vector nonlinearity in the mathematical description of the system. The problem of the number of cycle slippings is investigated. For both classes of control systems, frequency estimates of the deviation of each angular coordinate from its initial value are obtained. The estimation technique is based on the direct Lyapunov method with periodic Lyapunov functions. With the use of the Yakubovich-Kalman lemma, all results are formulated in terms of the transfer function of the linear part of the system. The results obtained have the form of frequency inequalities with variable parameters, which satisfy some algebraic inequalities.

UR - http://www.scopus.com/inward/record.url?scp=84859721324&partnerID=8YFLogxK

U2 - 10.3103/S1063454109010051

DO - 10.3103/S1063454109010051

M3 - Article

AN - SCOPUS:84859721324

VL - 42

SP - 28

EP - 36

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 49011745