  We present a model predictive control (MPC) scheme to control unknown 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 methods with a
numerical example.
