School of Mathematical Sciences, University College Cork, Cork, Republic of Ireland.
Philos Trans A Math Phys Eng Sci. 2013 Aug 19;371(1999):20120463. doi: 10.1098/rsta.2012.0463. Print 2013 Sep 28.
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.
我们提出了使用时滞反馈控制的扩展版本成功稳定周期轨道的一个必要条件。这个条件取决于实的 Floquet 乘子大于 1 的数量，因此与非自治系统中著名的奇数限制有关。我们表明，控制方案的时滞与未被控制轨道的周期失配所诱导的轨道的周期在自治情况下奇数限制的表述中起着重要作用。
