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This paper presents discussions on offset-free model predictive control (MPC) methods for linear discretetime systems in the presence of deterministic system disturbances. The general approach is based on the use of a disturbance model and an observer to estimate the disturbance states. The recent development in offset-free MPC has established the equivalence of the velocity form (without output delay) to a specific choice of the disturbance model and observer. In this note, it was shown that this particular disturbance model and observer is not necessarily equivalent to the velocity form with output delay. Nevertheless, it was shown that the velocity form with output delay is equivalent to a different choice of the disturbance model and observer. An import of this result is that the velocity forms (with and without delayed output) belong to the same general approach-disturbance model and observer. Furthermore, areas that may be considered in future researches are also highlighted.

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