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This paper presents a linear matrix inequality (LMI) method for the design of the wide-area time-delay damping (WATDD) controller of static synchronous series compensator (SSSC)-type flexible ac transmission system (FACTS) device to enhance the power stability of the interconnected power systems. Firstly, in order to reveal the single-input multi-output (SIMO) characteristic of the open-loop power system with SSSC-type FACTS device, the prediction error estimation (PEE) algorithm based system identification method is applied to fit a special SIMO linear model. Then, based on the robust control theory and LMI method, the identified linear model is formulated as the standard control problem with the time-delay of the input signals of the WATDD controller, and combined with the designed state observer for the input state variables of the WATDD controller, the control parameters are optimized by the LMI iterate solution algorithm. Finally, the nonlinear simulation on the typical 2-area 4-machine system installed with SSSC-type WATDD controller is performed to verify the LMI-based design method and the proposed SSSC-type WATDD controller.