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The lead-lag power system stabilizer has several parameters to be optimized.In fact, the number of these latter increases with the number of generators constituting the multi-machine system.In this work, we propose anew approach of an adaptive and robust PSS; it achieves encouraging results by adjusting the gain using fuzzy logic and in the same time we use the same PSSs for each machine. In the first place, we could check that the gain is among the most critical parameters of the lead lag PSS. The parameters are globally optimized by the genetic algorithm, after that an expertise on the speed and the gain variations allow the value prediction according to the velocity deviation. To validate our results, a robustness test was made on a multimachine system IEEE (3 machines 9 bus), for different loads and the results showed good performance and robustness of the presented PSS.