# Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables

arXiv: https://arxiv.org/abs/2301.12537 · HTML: https://mlsanity.com/paper/2301.12537/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Sample Complexity of the Sign-Perturbed Sums Method](https://mlsanity.com/paper/2409.01243/) (2024)
- [Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression](https://mlsanity.com/paper/2409.08801/) (2024)

## Abstract (arXiv)

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.