We show that a sufficient condition for the robust stability of
constrained linear model predictive control is for the plant to be
open-loop stable, for zero to be a feasible solution of the
associated quadratic programme and for the input weighting be
sufficiently high. The result can be applied equally to state
feedback and output feedback controllers with arbitrary prediction
horizon. If integral action is included a further condition on the
steady state modelling error is required for stability. We
illustrate the results with two forms of integral action commonly
used with model predictive control.