Rotating stall is a fundamental aerodynamic instability in axial how compressors, induced by nonlinear bifurcation. It effectively reduces the performance of aeroengines. In this paper classical bifurcation theory is used to derive output feedback control laws in which throttle position is employed as actuator and pressure rise as output measurement. The challenge to the proposed control system is that the critical mode of the linearized system corresponding to rotating stall is neither controllable nor observable. Using the projection method from Iooss and Joseph (1980), and Abed and Fu (1986), it is shown that linear output Feedback controllers are adequate for bifurcation stabilization. Both linear and nonlinear feedback control laws are proposed and are shown to be effective in elimination of hysteresis loop associated with rotating stall, and in extending the stable operating range of axial how compressors.