The Shell Standard Control Problem (SSCP), with its hard constraint specifications and the multiple performance objectives, is clearly the kind of problem to which the use of an on-line optimizing control algorithm like Quadratic Dynamic Matrix Control (QDMC) seems to be an appropriate approach. The presence of the hard constraints in the on-line optimization problem however, makes the overall system nonlinear even though the process dynamics are assumed linear. The Contraction Mapping Principle has been applied to the operator mapping the state of the system (plant + controller) at sampling point k to that at k + 1 to obtain nominal and robust stability conditions for the nonlinear system. These conditions can be used to analyze the stability properties of the QDMC algorithm and to obtain design insights by examining their variation during simulations of the system.