To take complete benefit of the Free Electron Laser (FEL) features, we have developed a feedback control scheme designed to suppress the dynamical instabilities affecting the FEL output intensity. The principle is to stabilize an unstable stationary state that coexists with the unwanted limit cycle. This paper gives a theoretical and experimental description of the stabilized stationary regime of a storage ring FEL in presence of the feedback control. We present a numerical model of the FEL with control, that describes the longitudinal dynamics of the laser pulse in condition of detuning between the FEL and the electron beam. These theoretical results are compared with experiments performed on the Super-ACO FEL. The established feedback control provides stable operation of the FEL.