Based on Moore and Greitzer's model (1986), the surge behavior is found to be attributed to the appearance of Hopf bifurcation. A Lyapunov function based control is proposed to provide the asymptotic stability of the post-surge operating point for the compressor with uncertain axisymmetric characteristic. Though the robust stabilization can be achieved by Lyapunov function based design, however, such an approach strongly relies on the explicit knowledge of the operating point. A washout filter type linear controller is proposed to delay and suppress the occurrence of Hopf bifurcation in compressor dynamics, which does not require the knowledge of system equilibria. Numerical results demonstrate the effectiveness of the proposed designs.