General features of stability domains for time-delayed feedback control exi
st, which can be predicted analytically. We clarify, why the control scheme
with a single delay term can only stabilise orbits with short periods or s
mall Lyapunov exponents, and derive a quantitative estimate. The limitation
can be relaxed by employing multiple delay terms. In particular, the exten
ded time delay autosynchronisation method is investigated in detail, Analyt
ic calculations are in good agreement with results of numerical simulations
and with experimental data from a nonlinear diode resonator, (C) 1999 Else
vier Science B.V.