Driveability, the ability to quickly respond to drivers action and a high degree of driving comfort is expected in a modern vehicle. Predictive control strategy in the discrete δ domain, in particular State Space δ GPC algorithm, reffered as SS δ GPC can bring significant improvements in terms of choosing a small sampling period. Moreover, this study is particularly relevant for implementation of control design on embedded systems, where the representation can be restricted to a finite number of bits. A δ state space affine model of automotive transmission system is used in order to illustrate the performances of the GPC design in the δ domain. The SS δ GPC is demonstrated to improve on the system response when it is compared with classical GPC using shift operator.