In this paper, a robust fuzzy digital PID control strategy, via multiobjective genetic algorithm, based on the gain and phase margins specifications, with applications to uncertain dynamic systems with time delay, is proposed. A mathematical formulation based on the gain and phase margins, the fuzzy model and PID digital controller structures, and the robust stability of the uncertain dinamic system with time delay, is deduced. A multiobjective genetic strategy is defined to tune the fuzzy

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... oller parameters, so the gain and phase margins specified to the fuzzy control system are get. It is proposed of two theorems related to necessary and suficient conditions for fuzzy robust digital control design. The first theorem enunciates that the robust PID controller in the i-th rule of the fuzzy robust digital PID controller guarantees the gain and phase margins specifications for the corresponding linear model. The second theorem enunciates that the robust PID controller in the i-th rule of the fuzzy robust digital PID controller guarantees the stability for all linear models. Experimental results shown the eficiency of the proposed methodology through tracking of the reference and the gain and phase margins keeping closed of the specified ones.