  We study the stability of unstable steady states in scalar retarded
time-delayed systems subjected to a variable-delay feedback control. The
important aspect of such a control problem is that time-delayed systems are
already infinite-dimensional before the delayed feedback control is turned on.
When the frequency of the modulation is large compared to the system's
dynamics, the analytic approach consists of relating the stability properties
of the resulting variable-delay system with those of an analogous distributed
delay system. Otherwise, the stability domains are obtained by a numerical
integration of the linearized variable-delay system. The analysis shows that
the control domains are significantly larger than those in the usual
time-delayed feedback control, and that the complexity of the domain structure
depends on the form and the frequency of the delay modulation.
