# Does open loop stability guarantee an MPC stability?

In the following publication

Arce, A., Alejandro, J., Bordons, C., & Ramirez, D. R. (2010).
"Real-time implementation of a constrained MPC for efficient
airflow control in a PEM fuel cell."
IEEE Transactions on Industrial Electronics, 57(6), 1892-1905.


There is a claim that

In fact, as the fuel cell is open-loop stable and the input signal is bounded, the closed-loop system is stable, at least in the bounded-input–bounded-output sense.

However, I doubt this claim is true for a Model Predictive Control (MPC). But, I do not have a counter example too.

Could anyone please inform if this claim is correct or any counter example exists.

• I think that open loop stability does not ensure the constraints will always be satisfied, for example when a too short horizon is used. Jul 19, 2018 at 3:10