A "fundamental lemma" for continuous-time systems, with applications to data-driven simulation

We are given one input-output (i-o) trajectory (u, y) produced by a linear, continuous time-invariant system, and we compute its Chebyshev polynomial series representation. We show that if the input trajectory u is sufficiently persistently exciting according to the definition in Rapisarda et al. (2023), then the Chebyshev polynomial series representation of every i-o trajectory can be computed from that of (u, y). We apply this result to data-driven simulation of continuous-time systems.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).