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The present paper proposes the application of robust control techniques for the development of a systematic methodology for the design of multiobjective controllers to damp low-frequency electromechanical oscillations in electric power systems. The control methodology adopted considers the uncertainties regarding the variations of the electric power system operating conditions with a technique known as polytopic modelling. The regional pole placement and the imposition of an upper bound for the output energy of the closed loop system are used as design objectives in the proposed methodology. The design methodology is structured to provide controllers that fulfil various practical requirements of the electromechanical oscillation problem in electric power systems. The presented results demonstrate the effectiveness of the designed controllers.