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 significantly reduces experiment time by eliminating the need to wait for transients to decay. 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 frequency-response-function evaluation at arbitrary frequencies in a numerical case study with and without noise.