Narrow Tilting Vehicles (NTVs) are the convergence of a car and a motorcycle. They are expected to be the new generation of city cars considering their practical dimensions and lower energy consumption. But considering their height to breadth ratio, in order to maintain lateral stability, NTVs should tilt when cornering. Unlike the motorcycle's case, where the driver tilts the vehicle himself, the tilting of an NTV should be automatic. The control objective in this paper is to reduce the perceived lateral acceleration through tilting, what would increase lateral stability and also the driver comfort with regard to centrifugal acceleration. A two degree of freedom tilting controller is proposed in the paper, using all the measurement available, controlling directly the perceived lateral acceleration (measured), while considering the steering angle as the main disturbance source. The control problem is recast as an optimal H2 problem, considering a model of the typical steering angle in addition to the vehicle model. The steering angle model allows predicting the near future of the vehicle trajectory, leading to an improved result in terms of energy requirements. Although initially designed for a given constant speed, the LPV controller is finally proposed with guaranties of good performance for a large range of speed and acceleration.