  Dissipativity properties have proven to be very valuable for systems analysis
and controller design. With the rising amount of available data, there has
therefore been an increasing interest in determining dissipativity properties
from (measured) trajectories directly, while an explicit model of the system
remains undisclosed. Most existing approaches for data-driven dissipativity,
however, guarantee the dissipativity condition only over a finite time horizon
and provide weak or no guarantees on robustness in the presence of noise. In
this paper, we present a framework for verifying dissipativity properties from
measured data with desirable guarantees. We first consider the case of
input-state measurements, where we provide non-conservative and computationally
attractive conditions in the presence of noise. We extend this approach to
input-output data, where similar results hold in the noise-free case. We then
provide results for the noisy input-output data case, which is particularly
challenging. Finally, we apply the proposed approach in a real-world experiment
and illustrate its applicability and advantages compared to established methods
based on system identification.
