A significant number of Model Based Process Control algorithms solve online an appropriate optimization problem and do so at every sampling point. The major attraction of such algorithms, like the Quadratic Dynamic Matrix Control (QDMC), lies in the fact that they can handle static nonlinearities in the form of hard constraints on the inputs (manipulated variables) of a process. The presence of such constraints as well as additional performance or safety induced hard constraints on certain outputs or states of the process, result in an on-line optimization problem that produces a nonlinear controller, even when the plant and model dynamics are assumed linear. This paper provides a theoretical framework within which the stability and performance properties of such algorithms can be studied.