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This paper presents a systematic method for the robust design of a supplementary controller for a TCSC device to damp inter-area oscillations in electric power systems. The method is based on a robust control technique structured in the form of linear matrix inequalities (LMIs). The polytopic model is used to guarantee the robustness of the controller with respect to the variations in the operating points of the system. The minimum damping ratio is used in the design stage as performance index for the closed loop system. The proposed controller is based on dynamic output feedback and uses only a local measurement of the active power flow as input signal for the controller, so communications links are avoided. The "feasp" solver, available in Matlab LMI Control Toolbox, is used to solve the set of LMIs formulated for the control problem. Performance analyses of the closed loop system were carried out by means of modal analysis and nonlinear simulations, showing that the controller is effective in improving the damping of inter-area oscillations of a two-area four-machine test system for several different operating points.