  We show explicitly the entropy reduction from a detailed fluctuation theorem
for the general stochastic system driven by nonequilibrium process under
feedback control. The effect of interaction of the feedback controller with the
system is to reduce the entropy of the system. We define the entropy reduction
for the single trajectory and show that the overall entropy production for the
stochastic system with feedback control can be either positive or negative. The
negative entropy production has been studied earlier for a simple system with
velocity dependent feedback control [K. H. Kim and H. Qian, Phys. Rev. Lett.
{\bf 93}, 120602 (2004)]. Our general approach provides the overall positive or
negative entropy production irrespective of velocity dependent and position
dependent feedback control.
