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Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem. / Leonov, G. A.; Shumafov, M. M.; Kuznetsov, N. V.

в: Differential Equations, Том 52, № 13, 01.12.2016, стр. 1707-1731.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Leonov, GA, Shumafov, MM & Kuznetsov, NV 2016, 'Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem', Differential Equations, Том. 52, № 13, стр. 1707-1731. https://doi.org/10.1134/S0012266116130036

APA

Leonov, G. A., Shumafov, M. M., & Kuznetsov, N. V. (2016). Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem. Differential Equations, 52(13), 1707-1731. https://doi.org/10.1134/S0012266116130036

Vancouver

Leonov GA, Shumafov MM, Kuznetsov NV. Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem. Differential Equations. 2016 Дек. 1;52(13):1707-1731. https://doi.org/10.1134/S0012266116130036

Author

Leonov, G. A. ; Shumafov, M. M. ; Kuznetsov, N. V. / Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem. в: Differential Equations. 2016 ; Том 52, № 13. стр. 1707-1731.

BibTeX

@article{552c3fd356be4550aee7ffc6f21082a9,
title = "Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem",
abstract = "A short survey on delayed feedback stabilization is given. The Huijberts–Michiels–Nijmeijer problem on the delayed feedback stabilization of unstable equilibria of two- and three-dimensional dynamical systems is considered. It is shown that the methods of delayed feedback stabilization of unstable periodic orbits can be used with advantage for the stabilization of unstable equilibria. An analytical study based on the D-decomposition method is given. Efficient necessary and/or sufficient conditions for the stabilizability of the systems in question are obtained in the form of explicit analytic expressions. These conditions define the boundaries of stabilizability domains in terms of system parameters. It follows from these conditions that the introduction of a delayed feedback control generally extends the possibilities of stationary stabilization of linear systems with delay-free feedback.",
keywords = "asymptotic stability, controllable system, delayed feedback control, stabilizability, unstable equilibrium",
author = "Leonov, {G. A.} and Shumafov, {M. M.} and Kuznetsov, {N. V.}",
year = "2016",
month = dec,
day = "1",
doi = "10.1134/S0012266116130036",
language = "English",
volume = "52",
pages = "1707--1731",
journal = "Differential Equations",
issn = "0012-2661",
publisher = "Pleiades Publishing",
number = "13",

}

RIS

TY - JOUR

T1 - Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem

AU - Leonov, G. A.

AU - Shumafov, M. M.

AU - Kuznetsov, N. V.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - A short survey on delayed feedback stabilization is given. The Huijberts–Michiels–Nijmeijer problem on the delayed feedback stabilization of unstable equilibria of two- and three-dimensional dynamical systems is considered. It is shown that the methods of delayed feedback stabilization of unstable periodic orbits can be used with advantage for the stabilization of unstable equilibria. An analytical study based on the D-decomposition method is given. Efficient necessary and/or sufficient conditions for the stabilizability of the systems in question are obtained in the form of explicit analytic expressions. These conditions define the boundaries of stabilizability domains in terms of system parameters. It follows from these conditions that the introduction of a delayed feedback control generally extends the possibilities of stationary stabilization of linear systems with delay-free feedback.

AB - A short survey on delayed feedback stabilization is given. The Huijberts–Michiels–Nijmeijer problem on the delayed feedback stabilization of unstable equilibria of two- and three-dimensional dynamical systems is considered. It is shown that the methods of delayed feedback stabilization of unstable periodic orbits can be used with advantage for the stabilization of unstable equilibria. An analytical study based on the D-decomposition method is given. Efficient necessary and/or sufficient conditions for the stabilizability of the systems in question are obtained in the form of explicit analytic expressions. These conditions define the boundaries of stabilizability domains in terms of system parameters. It follows from these conditions that the introduction of a delayed feedback control generally extends the possibilities of stationary stabilization of linear systems with delay-free feedback.

KW - asymptotic stability

KW - controllable system

KW - delayed feedback control

KW - stabilizability

KW - unstable equilibrium

UR - http://www.scopus.com/inward/record.url?scp=85014572328&partnerID=8YFLogxK

U2 - 10.1134/S0012266116130036

DO - 10.1134/S0012266116130036

M3 - Article

AN - SCOPUS:85014572328

VL - 52

SP - 1707

EP - 1731

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -

ID: 52006740