This paper is concerned with a novel control technique for automated lane keeping of a vehicle, which takes advantage of an exact fuzzy modelling of bounded parametric uncertainties—both constant and varying—for a convex treatment of local characteristic polynomials, put together via parameter-dependent Lyapunov analysis. It is shown that the specificity of the proposed technique enlarges the feasibility chances of synthesizing a robust steering control law in contrast with only-Lyapunov-based designs. The proposal is put at test in simulation for the perturbed bicycle model.