  In this paper we investigate data-driven predictive control of discrete-time
linear descriptor systems. Specifically, we give a tailored variant of Willems'
fundamental lemma, which shows that for descriptor systems the non-parametric
modelling via a Hankel matrix requires less data compared to linear
time-invariant systems without algebraic constraints. Moreover, we use this
description to propose a data-driven framework for optimal control and
predictive control of discrete-time linear descriptor systems. For the latter,
we provide a sufficient stability condition for receding-horizon control before
we illustrate our findings with an example.
