  Data-driven model predictive control (DD-MPC) based on Willems' Fundamental
Lemma has received much attention in recent years, allowing to control systems
directly based on an implicit data-dependent system description. The literature
contains many successful practical applications as well as theoretical results
on closed-loop stability and robustness. In this paper, we provide a tutorial
introduction to DD-MPC for unknown linear time-invariant (LTI) systems with
focus on (robust) closed-loop stability. We first address the scenario of
noise-free data, for which we present a DD-MPC scheme with terminal equality
constraints and derive closed-loop properties. In case of noisy data, we
introduce a simple yet powerful approach to analyze robust stability of DD-MPC
by combining continuity of DD-MPC w.r.t. noise with inherent robustness of
model-based MPC, i.e., robustness of nominal MPC w.r.t. small disturbances.
Moreover, we discuss how the presented proof technique allows to show
closed-loop stability of a variety of DD-MPC schemes with noisy data, as long
as the corresponding model-based MPC is inherently robust.
