  In this paper, we provide a theoretical analysis of closed-loop properties of
a simple data-driven model predictive control (MPC) scheme. The formulation
does not involve any terminal ingredients, thus allowing for a simple
implementation without (potential) feasibility issues. The proposed approach
relies on an implicit description of linear time-invariant systems based on
behavioral systems theory, which only requires one input-output trajectory of
an unknown system. For the nominal case with noise-free data, we prove that the
data-driven MPC scheme ensures exponential stability for the closed loop if the
prediction horizon is sufficiently long. Moreover, we analyze the robust
data-driven MPC scheme for noisy output measurements for which we prove
closed-loop practical exponential stability. The advantages of the presented
approach are illustrated with a numerical example.
