The automotive industry is facing many challenges related to different fields, in particular it is becoming more and more important the improvement of the technologies related to the reduction of emissions, fuel consumption and driving comfort. Considering all these factors, that are becoming crucial for the success of a new product, the companies are giving particular attention to the developement of more efficient transmission systems. The environmental needs and legislative pressure for a significant CO2 emissions reduction in the coming years forces the automotive industry to optimize every single component of the next generation vehicles. In this dissertation, realized in collaboration with Centro Ricerche Fiat (CRF), a Linear Quadratic Integral approach is implemented in order to control a Dry Dual Clutch Transmission system in hybrid vehicles with P2 architecture, during the slipping phase.