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Dissipativity properties have proven to be very valuable for systems analysisand controller design. With the rising amount of available data, there hastherefore been an increasing interest in determining dissipativity propertiesfrom (measured) trajectories directly, while an explicit model of the systemremains undisclosed. Most existing approaches for data-driven dissipativity,however, guarantee the dissipativity condition only over a finite time horizonand provide weak or no guarantees on robustness in the presence of noise. Inthis paper, we present a framework for verifying dissipativity properties frommeasured data with desirable guarantees. We first consider the case ofinput-state measurements, where we provide non-conservative and computationallyattractive conditions in the presence of noise. We extend this approach toinput-output data, where similar results hold in the noise-free case. We thenprovide results for the noisy input-output data case, which is particularlychallenging. Finally, we apply the proposed approach in a real-world experimentand illustrate its applicability and advantages compared to established methodsbased on system identification.

Provably robust verification of dissipativity properties from data