A short survey on Pyragas time-delay feedback stabilization and odd number limitation

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A short survey on Pyragas time-delay feedback stabilization and odd number limitation. / Kuznetsov, N. V.; Leonov, G. A.; Shumafov, M. M.

In: IFAC-PapersOnLine, Vol. 48, No. 11 11, 2015, p. 706-709.

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

BibTeX

@article{d4348e64e3884201be6d72c135462664,

title = "A short survey on Pyragas time-delay feedback stabilization and odd number limitation",

abstract = "K. Pyragas (1992) introduced a simple and eficient control scheme, called timedelayed feedback control (TDFC), that stabilizes unstable periodic orbit (UPO) embedded in a chaotic attractor. It turned out that in the case of Pyragas' stationary feedback TDFC works only for a certain class of systems. The odd number limitation (ONL) is that any UPO with an odd number of real Floquet multipliers greater than unity (or with odd number of real-positive Floquet exponents) can never be stabilized by Pyragas' TDFC. In this paper a short survey with recent results on TDFC and ONL is presented.",

keywords = "asymptotic stability, delayed feedback control, equilibrium, linear controllable system, stabilization",

author = "Kuznetsov, {N. V.} and Leonov, {G. A.} and Shumafov, {M. M.}",

note = "Publisher Copyright: {\textcopyright} 2015",

year = "2015",

doi = "10.1016/j.ifacol.2015.09.271",

language = "English",

volume = "48",

pages = "706--709",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "11 11",

}

RIS

TY - JOUR

T1 - A short survey on Pyragas time-delay feedback stabilization and odd number limitation

AU - Kuznetsov, N. V.

AU - Leonov, G. A.

AU - Shumafov, M. M.

PY - 2015

Y1 - 2015

N2 - K. Pyragas (1992) introduced a simple and eficient control scheme, called timedelayed feedback control (TDFC), that stabilizes unstable periodic orbit (UPO) embedded in a chaotic attractor. It turned out that in the case of Pyragas' stationary feedback TDFC works only for a certain class of systems. The odd number limitation (ONL) is that any UPO with an odd number of real Floquet multipliers greater than unity (or with odd number of real-positive Floquet exponents) can never be stabilized by Pyragas' TDFC. In this paper a short survey with recent results on TDFC and ONL is presented.

AB - K. Pyragas (1992) introduced a simple and eficient control scheme, called timedelayed feedback control (TDFC), that stabilizes unstable periodic orbit (UPO) embedded in a chaotic attractor. It turned out that in the case of Pyragas' stationary feedback TDFC works only for a certain class of systems. The odd number limitation (ONL) is that any UPO with an odd number of real Floquet multipliers greater than unity (or with odd number of real-positive Floquet exponents) can never be stabilized by Pyragas' TDFC. In this paper a short survey with recent results on TDFC and ONL is presented.

KW - asymptotic stability

KW - delayed feedback control

KW - equilibrium

KW - linear controllable system

KW - stabilization

UR - http://www.scopus.com/inward/record.url?scp=84992491230&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2015.09.271

DO - 10.1016/j.ifacol.2015.09.271

M3 - Article

AN - SCOPUS:84992491230

VL - 48

SP - 706

EP - 709

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 11 11

ER -

ID: 95263801