Beyond the odd number limitation: A bifurcation analysis of time-delayed feedback control

2007 ◽  
Vol 76 (2) ◽  
Author(s):  
W. Just ◽  
B. Fiedler ◽  
M. Georgi ◽  
V. Flunkert ◽  
P. Hövel ◽  
...  
Keyword(s):  
Feedback Control ◽  
Bifurcation Analysis ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Odd Number Limitation ◽  
Time Delayed Feedback

Beyond the Odd-Number Limitation of Time-Delayed Feedback Control

2008 ◽  
pp. 73-84 ◽  
Author(s):  
Bernold Fiedler ◽  
Valentin Flunkert ◽  
Marc Georgi ◽  
Philipp Hvel ◽  
Eckehard Schll
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Odd Number Limitation ◽  
Time Delayed Feedback

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

2013 ◽  
Vol 371 (1999) ◽  
pp. 20120463 ◽  
Author(s):  
Andreas Amann ◽  
Edward W. Hooton
Keyword(s):  
Feedback Control ◽  
Autonomous Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Necessary Condition ◽  
Floquet Multipliers ◽  
Control Scheme ◽  
Autonomous Case ◽  
Odd Number Limitation ◽  
Time Delayed Feedback

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.

scholarly journals Refuting the Odd-Number Limitation of Time-Delayed Feedback Control

2007 ◽  
Vol 98 (11) ◽  
Author(s):  
B. Fiedler ◽  
V. Flunkert ◽  
M. Georgi ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Odd Number Limitation ◽  
Time Delayed Feedback
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