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The predictive control developments in the literature, in particular those giving a priori stability guarantees, have often been based on realigned models whereas industrial packages have often made much use of independent models. However, the transferal of many of these stability results to the independent model case is not straightforward especially for the important case of unstable open-loop processes. This note shows how terminal constraints can be deployed with unstable independent models and illustrates briefly the necessity and benefits of these developments.