Leveraging Non-Steady-State Frequency-Domain Data in Willems' Fundamental Lemma

Willems’ fundamental lemma enables data-driven analysis and control by characterizing an unknown system’s behavior directly in terms of measured data. In this work, we extend a recent frequency-domain variant of this result–previously limited to steady-state data–to incorporate non-steady-state data including transient phenomena. This approach eliminates the need to wait for transients to decay during data collection, significantly reducing the experiment duration. Unlike existing frequency-domain system identification methods, our approach integrates transient data without preprocessing, making it well-suited for direct data-driven analysis and control. We demonstrate its effectiveness by isolating transients in the collected data and performing FRF evaluation at arbitrary frequencies in a numerical case study including noise.