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In this paper, we investigate the verification of dissipativity propertiesfor polynomial systems without an explicitly identified model but directly fromnoise-corrupted measurements. Contrary to most data-driven approaches fornonlinear systems, we determine dissipativity properties over all finite timehorizons using noisy input-state data. To this end, we propose two noisecharacterizations to deduce two data-based set-membership representations ofthe ground-truth system. Each representation then serves as a framework toderive computationally tractable conditions to verify dissipativity propertieswith rigorous guarantees from noise-corrupted data using sum of squares (SOS)optimization.

Dissipativity verification with guarantees for polynomial systems from noisy input-state data