  Given one open-loop measured trajectory of a single-input single-output
discrete-time linear time-invariant system, we present a framework for
data-driven controller design for closed-loop finite-horizon dissipativity.
First, we parametrize all closed-loop trajectories using the given data of the
plant and a model of the controller. We then provide an approach to validate
the controller by verifying closed-loop dissipativity in the standard feedback
loop based on this parametrization. We use these conditions to design
controllers leading to closed-loop dissipativity based on a quadratic matrix
inequality feasibility problem. Finally, the results are illustrated with a
simulation example.
