  The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite
sample system identification method for the identification of closed-loop
observable stochastic linear systems in state-space form. The solution builds
on the theory of matrix-variate regression and instrumental variable methods to
construct distribution-free confidence regions for the state-space matrices.
Both direct and indirect identification are studied, and the exactness as well
as the strong consistency of the construction are proved. Furthermore, a new,
computationally efficient ellipsoidal outer-approximation algorithm for the
confidence regions is proposed. The new construction results in a semidefinite
optimization problem which has an order-of-magnitude smaller number of
constraints, as if one applied the ellipsoidal outer-approximation after
vectorization. The effectiveness of the approach is also demonstrated
empirically via a series of numerical experiments.
