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An H∞-mixed-sensitivity design of a damping device employing a unified-power-flow controller (UPFC) is presented. The problem is posed in the linear-matrix-inequality (LMI) framework. The controller design is aimed at providing adequate damping to interarea oscillations over a range of operating conditions. The results obtained in a two-area four-machine test system are seen to be very satisfactory both in the frequency domain and through nonlinear simulations.