  We study the identification of a linear time-invariant dynamical system
affected by large-and-sparse disturbances modeling adversarial attacks or
faults. Under the assumption that the states are measurable, we develop
necessary and sufficient conditions for the recovery of the system matrices by
solving a constrained lasso-type optimization problem. In addition, we provide
an upper bound on the estimation error whenever the disturbance sequence is a
combination of small noise values and large adversarial values. Our results
depend on the null space property that has been widely used in the lasso
literature, and we investigate under what conditions this property holds for
linear time-invariant dynamical systems. Lastly, we further study the
conditions for a specific probabilistic model and support the results with
numerical experiments.
