  We present a model predictive control (MPC) scheme to control linear
time-invariant systems using only measured input-output data and no model
knowledge. The scheme includes a terminal cost and a terminal set constraint on
an extended state containing past input-output values. We provide an explicit
design procedure for the corresponding terminal ingredients that only uses
measured input-output data. Further, we prove that the MPC scheme based on
these terminal ingredients exponentially stabilizes the desired setpoint in
closed loop. Finally, we illustrate the advantages over existing data-driven
MPC approaches with a numerical example.
