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

Rapisarda, P., Camlibel, M.K. and van Waarde, H.J. (2023) A “fundamental lemma” for continuous-time systems, with applications to data-driven simulation. Systems & Control Letters, 179, [105603]. (doi:10.1016/j.sysconle.2023.105603).

Record type: Article

Abstract

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.

Text

SSRN-id4370211 (1) - Author's Original

Restricted to Repository staff only

Request a copy

Text

CTLemmaRevisedV6 - Accepted Manuscript

Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (197kB)

Text

1-s2.0-S0167691123001500-main - Version of Record

Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (478kB)

More information

Accepted/In Press date: 20 July 2023

e-pub ahead of print date: 7 August 2023

Published date: September 2023

Keywords: Chebyshev polynomials, Persistency of excitation, continuous-time linear time-invariant systems,, data-driven simulation, Continuous-time linear time-invariant systems, Data-driven simulation

Learn more about Electrical Power Engineering research