Lately, with the increasing use of automated manual transmissions (AMT) the engagement control of the dry clutch becomes more important. The engagement control plays a crucial role, since different and conflicting objectives have to be satisfied: preservation of driver comfort, fast engagement and small friction losses. In this paper two optimal control strategies for clutch engagement, based on hybrid control principles, are compared. For developing a useful clutch control scheme, the driveline is modelled as a piecewise linear system. The first control strategy is widely known as explicit MPC. However, it seems that it is not suitable (yet) for this type of problem. The second strategy is a piecewise LQ controller, based on piecewise quadratic Lyapunov functions. Simulation results obtained with both strategies are presented and discussed.