In this diploma theses a recently developed controller design (explicit MPC) is used for the airpath control of a diesel engine. The explicit solution of linear quadratic regulator (LQR) with constraints offers the opportunity of calculating the explicit solution of the state feedback control law offline and storing it in tables for online controller selection (Look Up Tables). So the computational expense can be shifted from online to offline calculation which is essential for high speed applications like engine control. The combination of plant and switched controller leads to a piecewise linear and discrete system - a special form of hybrid system.