  When stabilization of unstable periodic orbits or fixed points by the method
given by Ott, Grebogi and Yorke (OGY) has to 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 Ljapunov number of
$\lambda_{max}=1+\frac{1}{\tau}$. 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 have to be
considered if one wants to stabilize fixed points with Ljapunov numbers above
$\lambda_{max}$.

Chaotic Dynamics