Variable damping shock absorbers have received extensive attention for their efficient vibration reduction performance, and air springs have also been widely used in high-end commercial vehicles due to their nonlinear stiffness characteristics. This paper presents a novel semi-active cab suspension integrated with an air spring and a variable damping electromagnetic damper (A-EMD). The electromagnetic damper (EMD) prototype was designed, manufactured and tested. Then, due to the interference of nonlinear stiffness characteristics of the air spring with the controller in the subsequent design, the Takagi–Sugeno fuzzy method was adopted to segmentally linearize its nonlinearity, based on which an H∞ state feedback semi-active controller was designed to control the EMD to generate variable damping force. Furthermore, a Luenberger state observer was designed to provide immeasurable state parameters for the controller. Numerical simulations were carried out to validate the effectiveness of the proposed approaches, and the results show that the proposed control strategy can significantly improve the ride comfort of the A-EMD system. The vibration dose value (VDV) acceleration under the bump road and the frequency-weighted acceleration root mean square (FWA-RMS) under the random road decreased by 36.05% and 19.77%, respectively, compared with the passive suspension system.