An odd-number limitation of extended time-delayed feedback control in autonomous systems

被引：15
|
作者：
Amann, Andreas [1 ,2 ]
Hooton, Edward W. [1 ]
机构：
[1] Univ Coll Cork, Sch Math Sci, Cork, Ireland
[2] Univ Coll Cork, Tyndall Natl Inst, Cork, Ireland
来源：
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2013年 / 371卷 / 1999期
基金：
爱尔兰科学基金会;
关键词：
time delay; chaos control; Floquet theory; PERIODIC-ORBITS; CHAOS;
D O I：
10.1098/rsta.2012.0463
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We propose a necessary condition for the successful stabilization of a periodic orbit, using the extended version of time-delayed feedback control. This condition depends on the number of real Floquet multipliers larger than unity and is therefore related to the well-known odd-number limitation in non-autonomous systems. We show that the period of the orbit that is induced by mismatching the delay time of the control scheme and the period of the uncontrolled orbit plays an important role in the formulation of the odd-number limitation in the autonomous case.
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页数：8
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