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The present paper proposes an alternative performance index for the design of robust controllers to damp low-frequency electromechanical oscillations in power systems. The concept of output energy is used as performance index as opposed to the usual criterion of minimum damping ratio. The control problem with both performance indices was structured in the form of linear matrix inequalities and it was verified that the formulation with the output energy is less costly in terms of computational effort when compared to the one with the traditional minimum damping ratio. This characteristic allows the application of the proposed methodology to controller design involving large power system models. The design methodology is based on a multimachine model, without requiring the assumption that some part of the system can be modelled as an infinite bus. Such assumption is usual in control designs based on many modern control techniques, and may modify the dynamics described by the system model and consequently affect the performance of the designed controllers. The design methodology provides controllers that fulfill various practical requirements of the oscillation problem. The methodology has provided effective controllers with acceptable performance as shown in the results, and the gain in computational time was significant.