A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.
Dmitrishin, Dmitriy, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos.
"Fejér and Suffridge Polynomials in the Delayed Feedback Control Theory."
arXiv Repository: 1-34.