  This paper investigates the ability of the stochastic subspace identification
technique to return a valid model from finite measurement data, its asymptotic
properties as the data set becomes large, and asymptotic error bounds of the
identified model (in terms of $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$
norms). First, a new and straightforward LMI-based approach is proposed, which
returns a valid identified model even in cases where the system poles are very
close to unit circle and there is insufficient data to accurately estimate the
covariance matrices. The approach, which is demonstrated by numerical examples,
provides an altenative to other techniques which often fail under these
circumstances. Then, an explicit expression for the variance of the
asymptotically normally distributed sample output covariance matrices and
block-Hankel matrix are derived. From this result, together with perturbation
techniques, error bounds for the state-space matrices in the innovations model
are derived, for a given confidence level. This result is in turn used to
derive several error bounds for the identified transfer functions, for a given
confidence level. One is an explicit $\mathcal{H}_2$ bound. Additionally, two
$\mathcal{H}_{\infty}$ error bounds are derived, one via perturbation analysis,
and the other via an LMI-based technique.
