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. [ABSTRACT FROM AUTHOR]