We present a linear analysis for a recently proposed modification of t
he delay feedback control technique that allows one to stabilize unsta
ble periodic orbits of a strange attractor over a large domain of para
meters. The method uses a continuous feedback loop incorporating infor
mation from many previous states of the system in a form closely relat
ed to the amplitude of light reflected from a Fabry-Perot interferomet
er. We illustrate the possibility of stabilizing high-periodic orbits
and fixed points with large values of Lyapunov exponents.