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

Dissipativity Verification With Guarantees for Polynomial Systems From Noisy Input-State Data