TY - JOUR
T1 - A “fundamental lemma” for continuous-time systems, with applications to data-driven simulation
AU - Rapisarda, P.
AU - Çamlibel, M. K.
AU - van Waarde, H. J.
N1 - Publisher Copyright:
© 2023 The Author(s)
PY - 2023/9
Y1 - 2023/9
N2 - 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.
AB - 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.
KW - Chebyshev polynomials
KW - Continuous-time linear time-invariant systems
KW - Data-driven simulation
KW - Persistency of excitation
UR - http://www.scopus.com/inward/record.url?scp=85166979028&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2023.105603
DO - 10.1016/j.sysconle.2023.105603
M3 - Article
AN - SCOPUS:85166979028
SN - 0167-6911
VL - 179
JO - Systems and Control Letters
JF - Systems and Control Letters
M1 - 105603
ER -