  This paper addresses the problem of identifying sparse linear time-invariant
(LTI) systems from a single sample trajectory generated by the system dynamics.
We introduce a Lasso-like estimator for the parameters of the system, taking
into account their sparse nature. Assuming that the system is stable, or that
it is equipped with an initial stabilizing controller, we provide sharp
finite-time guarantees on the accurate recovery of both the sparsity structure
and the parameter values of the system. In particular, we show that the
proposed estimator can correctly identify the sparsity pattern of the system
matrices with high probability, provided that the length of the sample
trajectory exceeds a threshold. Furthermore, we show that this threshold scales
polynomially in the number of nonzero elements in the system matrices, but
logarithmically in the system dimensions --- this improves on existing sample
complexity bounds for the sparse system identification problem. We further
extend these results to obtain sharp bounds on the $\ell_{\infty}$-norm of the
estimation error and show how different properties of the system---such as its
stability level and \textit{mutual incoherency}---affect this bound. Finally,
an extensive case study on power systems is presented to illustrate the
performance of the proposed estimation method.
