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An optimal decentralised design for output-feedback power-system stabilisers (PSSs) is presented. The PSS design problem is converted to an optimisation problem. A system dynamics-objective function is established and the derivations of an explicit expression for this function are given. Considerations for a stable system, the relative stability of low-frequency modes and the practical implementation of PSSs are all included in the constraints. Guidelines for choosing weighting factors affecting system performance are suggested. Only local and available state variables are adopted as the input signals of each PSS for the decentralised design. Output-feedback gains of the stabilisers can be obtained by using genetic algorithms. Structures of the designed PSSs are simple and easy to implement. The design process has considered different operating conditions. Three methods of assessment: eigenvalue analyses, time-domain simulations and total dynamic indices, are performed on a multimachine power system. Test results demonstrate the possibility of the proposed design applied to multimachine power systems to damp system oscillations.