Time-delay brought by wide-area communication is one of the most important causes leading to the performance degradation and even the failure of the controllers. The motion equation of the generator rotors of the multi-machine power system is linearized and deviated in the paper, in consideration of the characteristics of the time-delay power system. Then, defining a proper Lyapunov function, stabilization criteria based on the linear matrix inequality theory are presented by introducing some weight-free matrices. And the controller with full state feedback is designed. Compared to the linear quadratic optimal control, the controller is less conservative and more effective. The validity of the controller is verified by the IEEE 3-machine 9-bus test system. The simulation results show that the controller can reduce the negative impact caused by the time-delays.