Compressor stall and surge are complex nonlinear instabilities that reduce the performance and can cause failure of aircraft engines. We design a feedback controller that globally stabilizes a broad range of possible equilibria in a nonlinear compressor model. With a novel backstepping design we retain the system＇s useful nonlinearities which would be cancelled in a feedback linearizing design. The design control law is simple and, moreover, it is optimal with respect to a meaningful nonquadratic cost functional. As in a previous bifurcation-theoretic design, we change the character of the bifurcation at the stall inception point from subcritical to supercritical. However, since we do not approach bifurcation control using a normal form but using Lyapunov tools, our controller achieves not only local but also global stability. The controller requires minimal modeling information (bounds on the slope of the stud characteristic and the B-parameter) and simpler sensing (rotating stall is stabilized without measuring its amplitude).