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.

N1 - Publisher Copyright: © 2015

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 - 2405-8971

IS - 11 11

ER -