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This study develops a new method by which the controller output limits are taken into account in the eigenvalue-based control coordination design for achieving optimal dampings of the electromechanical oscillations for specified disturbances. The method combines the non-linear time-domain simulations with the constrained optimisation of the eigenvalue-based objective function. The time-domain simulations are used to derive the linearised relations between the maximum controllers outputs and controllers parameters, for any specified disturbances. The relations combined with specified controller output limits lead to additional set of constraints in the design. The time-domain simulations are performed independent of one another and outside the optimisation procedure. These features lead to lower computing time requirement and the possibility of using parallel processors for implementing the design algorithm. From many design studies in which linearised relations are derived and used, the number of constrained optimisations required is relatively low (about 5). The results of representative design cases with a multimachine power system having power system stabilisers and supplementary damping controllers of thyristor-controlled series capacitors are presented. The performance of the designed controllers is verified by non-linear time-domain simulations.