Limitation of generalized delayed feedback control

✍ Scribed by Hiroyuki Nakajima; Yoshisuke Ueda

• Book ID: 104297412
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 383 KB
• Volume: 111
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)80009-7

✦ Synopsis

It had been proved that the delayed feedback control (DFC) of chaos has a limitation as follows: If the linear variational equation about the target hyperbolic unstable periodic orbit (UPO) has an odd number of real characteristic multipliers greater than unity, the UPO can never be stabilized by the DFC with any value of feedback gain. We show that this limitation also holds for generalized DFCs based on the feedback of the difference between the current state and delayed states, which include the extended time-delay auto-synchronization (ETDAS) and an exponential DFC.