  Identifying a linear system model from data has wide applications in control
theory. The existing work on finite sample analysis for linear system
identification typically uses data from a single system trajectory under i.i.d
random inputs, and assumes that the underlying dynamics is truly linear. In
contrast, we consider the problem of identifying a linearized model when the
true underlying dynamics is nonlinear. We provide a multiple trajectories-based
deterministic data acquisition algorithm followed by a regularized least
squares algorithm, and provide a finite sample error bound on the learned
linearized dynamics. Our error bound demonstrates a trade-off between the error
due to nonlinearity and the error due to noise, and shows that one can learn
the linearized dynamics with arbitrarily small error given sufficiently many
samples. We validate our results through experiments, where we also show the
potential insufficiency of linear system identification using a single
trajectory with i.i.d random inputs, when nonlinearity does exist.
