This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems that can be modeled by the first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi–Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. First, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Second, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows us to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor.