Stability borders of feedback control of delayed measured systems.
When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi, and Yorke (OGY) must be based on a measurement delayed by tau orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Lyapunov number of lambda(max) =1+ ( 1/tau ) . In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions must be considered if one wants to stabilize fixed points with Lyapunov numbers above lambda(max) .
Claussen
Jens Christian
JC
Institut für Theoretische Physik und Astrophysik der Universität Kiel, 24098 Kiel, Germany.