  In this paper we study the stabilization of rotating waves using time delayed
feedback control. It is our aim to put some recent results in a broader context
by discussing two different methods to determine the stability of the target
periodic orbit in the controlled system: 1) by directly studying the Floquet
multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an
extension of the Pyragas control scheme for which the controlled system becomes
a functional differential equation of neutral type. Using the observation that
we are able to determine the direction of bifurcation by a relatively simple
calculation of the root tendency, we find stability conditions for the periodic
orbit as a solution of the neutral type equation.
