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The paper proposes analytical method for design of multiple fuzzy logic controllers (FLC) in a multi machine power system to enhance system damping and stability. The proposed method is independent of a priori information about the system performance that should be provided by human expert (operator). As such it is more general and more straight forward for application than the other FLC design methods proposed in the past. The design of FLCs is described in detail and the performance and robustness of the controllers is tested and demonstrated on a four generator eight bus asymmetrical power system. The practical implementation issues of FLC controllers are also discussed.