We consider the classical 3-state Moore-Greitzer model, which is commonly used for approximating dynamics of deviations of flow and pressure variables in an axial compressor from their nominal steady-state values. The linearization of the nonlinear system is not controllable and, therefore, even local asymptotic stability cannot be achieved using methods of linear control theory. We propose a family of parametrized partialstate feedback control laws and derive sufficient conditions to guarantee global asymptotic stability of the closed-loop system. The stability analysis uses the integral quadratic constraints technique for the case of non-strict frequency condition and novel arguments for characterization of omega-limit sets.