Stability of Model Predictive Control with Soft Constraints

We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and \soft" constraints on the outputs for an innnitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The on-line optimization problem deening MPC can be posed as a nite dimensional quadratic program even though the output constraints are speciied over an innnite horizon.