# Maximum MPC prediction horizon for an unstable plant

In the following book,

Model Predictive Control ToolboxTM (User's Guide)

Manfred Morari
N. Lawrence Ricker


At page 1-6, it has been mentioned that

If the plant is open-loop unstable, the maximum possible p is the number of control intervals required for the plant’s open-loop step response to become infinite.

Here, p means the prediction horizon.

This claim does not look reasonable to me. I have not understood the reason for this claim. What will happen if I choose the prediction horizon longer?