  This note extends a recently proposed algorithm for model identification and
robust MPC of asymptotically stable, linear time-invariant systems subject to
process and measurement disturbances. Independent output predictors for
different steps ahead are estimated with Set Membership methods. It is here
shown that the corresponding prediction error bounds are the least conservative
in the considered model class. Then, a new multi-rate robust MPC algorithm is
developed, employing said multi-step predictors to robustly enforce constraints
and stability against disturbances and model uncertainty, and to reduce
conservativeness. A simulation example illustrates the effectiveness of the
approach.
