A correction to "Min-max predictive control strategies for input-saturated polytopic uncertain systems" [Automatica 36 (2000) 125-133]

with N the control horizon, x(t + k|t) the set-valued k-step ahead state prediction and F the terminal feasible and robustly stabilizing state-feedback. In Lemma 2 and Main Result of Casavola et al. (2000) it was erroneously claimed that the regions of attraction are nested, viz. the region for N + 1 includes the one corresponding to N. This can be shown to be untrue in general by counterexamples. As discussed in Mayne, Rawlings, Rao, and Scokaert (2000), the flaw hinges upon the poor feasibility properties of open-loop MPC solutions in the presence of polytopic model uncertainties. There are several ways for recovering the feasibility and all other properties stated in the Lemma 2 and Main Result of Casavola et al. (2000). The one that will be described in this note appears as the simplest one in that it only consists of slightly modifying the earlier formulation with no increase of computational load. The amended formulation uses, instead of (1), a so-called feedback control policy. The latter consists, in its simplest form, of adopting a control strategy of the form