This paper studies the control strategies for enhancing the transient stability of a single machine infinite bus (SMIB) power system. First, the dynamical SMIB model is established, and the excitation control is discussed. Next, the damping linear optimal excitation controller (DLOEC) and the output feedback H_infinity control strategy are studied. Then, the DLOEC and the suboptimum H_infinity controller are designed for a specific SMIB power system. The effectiveness of the two presented methods is verified by simulations. The simulation results show that the presented methods improve the transient stability of the SMIB power system and that the H_infinity controller provides better performance than the DLOEC controller.