  The focus of this paper is on linear system identification in the setting
where it is known that the underlying partially-observed linear dynamical
system lies within a finite collection of known candidate models. We first
consider the problem of identification from a given trajectory, which in this
setting reduces to identifying the index of the true model with high
probability. We characterize the finite-time sample complexity of this problem
by leveraging recent advances in the non-asymptotic analysis of linear
least-square methods in the literature. In comparison to the earlier results
that assume no prior knowledge of the system, our approach takes advantage of
the smaller hypothesis class and leads to the design of a learner with a
dimension-free sample complexity bound. Next, we consider the switching control
of linear systems, where there is a candidate controller for each of the
candidate models and data is collected through interaction of the system with a
collection of potentially destabilizing controllers. We develop a
dimension-dependent criterion that can detect those destabilizing controllers
in finite time. By leveraging these results, we propose a data-driven switching
strategy that identifies the unknown parameters of the underlying system. We
then provide a non-asymptotic analysis of its performance and discuss its
implications on the classical method of estimator-based supervisory control.
