With the expansion of the power system, the timedelay of control signal generated in the widearea environment will produce a negative effects that can not be neglected for the stable operation of power system. Based on Lyapunov stability theory, the design problems of widearea power system state feedback controller with timedelay was studied in this paper. Firstly, by constructing a Lyapunov Krasovskii functional, using matrix resolution method, we derive a matrix inequality structure based on the nonlinear. Then, transforming the nonlinear matrix inequality into linear matrix inequality, it is converted to a cone complementarity problem subjecting to linear matrix inequality and solved by iteration, the timedelay upper bounds and the iteration times is balanced by optimization iIterative algorithm. Finally, simulation results indicated that the controller derived in the paper has less conservatism and faster speed, and better project practicality.