  In this paper, a method to represent every input-output trajectory of a
continuous-time linear system in terms of previously collected data is
presented. This corresponds to a continuous-time version of the well-known
Willems' lemma. The result is obtained by sampling the continuous signals at
regular intervals, and constructing Hankel-like structures that closely
resemble their discrete-time counterparts. Then, it is shown how to use
measured persistently excited data to design a time-varying vector of
parameters that allows the generation of arbitrary piecewise differentiable
trajectories. A class of input signals that satisfies the conditions for
persistence of excitation is also provided.
