Robustness of Type-l fuzzy logic power system stabilizers (FLPSSs) often lacks mathematical reasoning where the performance of such a stabilizer is often reviewed by transient response of the closed loop system. Necessary and sufficient conditions that guarantee robust dynamic stability of an FLPSS are presented. A small-signal model of an FLPSS is developed to study the dynamic stability of a single-machine infinite-bus power system. Such a small signal model is proved to be a conventional proportional-derivative (PD) controller whose parameters are expressed in terms of normalizing factors of FLPSS. The parameters of such a PD controller, are tuned to guarantee robust dynamic stability, thereafter normalizing factors can be directly computed. Synthesis of a robust PD controller is based on simultaneous stabilization of a finite number of extreme characteristic polynomials. Such polynomials are derived using Kharitonov theorem from an interval polynomial considered to reflect effect of loading conditions on characteristic polynomial coefficients. A convex region in the Kp-Kd parameter plane which guarantees robust stability is obtained using Routh-Hurwitz array. Such a region presents the pool for all robust normalizing factors of an FLPSS. Simulation results are presented to confirm the effectiveness of the proposed approach.