  Predictive control, which is based on a model of the system to compute the
applied input optimizing the future system behavior, is by now widely used. If
the nominal models are not given or are very uncertain, data-driven model
predictive control approaches can be employed, where the system model or input
is directly obtained from past measured trajectories. Using a data
informativity framework and Finsler's lemma, we propose a data-driven robust
linear matrix inequality-based model predictive control scheme that considers
input and state constraints. Using these data, we formulate the problem as a
semi-definite optimization problem, whose solution provides the matrix gain for
the linear feedback, while the decisive variables are independent of the length
of the measurement data. The designed controller stabilizes the closed-loop
system asymptotically and guarantees constraint satisfaction. Numerical
examples are conducted to illustrate the method.
