Abstract: There exists time delay problem in solving the inter-area low-frequency oscillation of power system, which brings significant influence on the system stability. In order to solve this problem, a reduced-order mathematical model of power system is firstly established. And then a tradeoff-based idea is proposed to achieve wide-area damping control. Based on the linear matrix inequality (LMI) toolbox, the Lyapunov time-delay stability criterion is used to acquire the wide-area damping controller (WADC) parameters. And then the system stability is proved by using an indirect method of time-delay segmentation, and the damping characteristics of the power system is analyzed. Finally, simulations are carried out by using the four-machine two-area model. The simulation results show that the rotor angle and reactive power tend basically stable in about 6 seconds, and the damping stability of power system is improved effectively compared with other conventional WADC methods.