  Data-driven methods for modeling dynamic systems have received considerable
attention as they provide a mechanism for control synthesis directly from the
observed time-series data. In the absence of prior assumptions on how the
time-series had been generated, regression on the system model has been
particularly popular. In the linear case, the resulting least squares setup for
model regression, not only provides a computationally viable method to fit a
model to the data, but also provides useful insights into the modal properties
of the underlying dynamics. Although probabilistic estimates for this model
regression have been reported, deterministic error bounds have not been
examined in the literature, particularly as they pertain to the properties of
the underlying system. In this paper, we provide deterministic non-asymptotic
error bounds for fitting a linear model to the observed time-series data, with
a particular attention to the role of symmetry and eigenvalue multiplicity in
the underlying system matrix.
