Stability of periodic waves generated by subcritical oscillatory instability under the action of feedback control

Periodic solutions of a subcritical cubic complex Ginzburg-Landau equation are considered in the limit of large dispersion and nonlinear frequency shift. Results obtained formerly by Schöpf and Kramer are revisited and extended to the case of a defocusing nonlinearity. It is shown that a global feedback control can extend existence and stability regions of the stationary solutions in both focusing and defocusing cases.