  We illustrate a novel version of Willems' lemma for data-based representation
of continuous-time systems. The main novelties compared to previous works are
two. First, the proposed framework relies only on measured input-output
trajectories from the system and no internal (state) information is required.
Second, our system representation makes use of exact system trajectories,
without resorting to orthogonal bases representations and consequent
approximations. We first establish sufficient and necessary conditions for
data-based generation of system trajectories in terms of suitable latent
variables. Subsequently, we reformulate these conditions using measured
input-output data and show how to span the full behavior of the system.
Furthermore, we show how to use the developed framework to solve the data-based
continuous-time simulation problem.
