A fuzzy-H∞ control, improved with weighting functions, has been designed and applied to a novel model of a one-half semiactive lateral vehicle (OHSLV) suspension. The herein contribution resides in the development and computation of an H∞ controller with parallel distributed compensation (PDC) designed from a highly nonlinear system modelled via the Takagi-Sugeno (T-S) fuzzy approach. A fuzzy-H∞ controller is synthesized for an OHSLV T-S fuzzy model of a suspension with two magnetorheological (MR) dampers including actuators' nonlinear dynamics. The realism of results has been improved by considering the MR damper's behaviours (viscoplasticity, hysteresis, and saturation) and the handling of the phase angle of the sinusoidal disturbance, not included in other reported work. Time-domain tests remark transient time achievements, whereas precise performance criterion indices in the frequency domain are employed to assess the generated outcomes. The proposed solution complies with all performance criteria compared with a benchmark passive average suspension that fails in satisfying most of the performance criteria.