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.

翻译：本文提出了符号扰动和（SPS）有限样本系统辨识方法的一种推广，用于辨识状态空间形式的闭环可观测随机线性系统。该解基于矩阵变量回归理论和工具变量方法，构建状态空间矩阵的无分布置信域。研究了直接辨识与间接辨识两种方式，并证明了构造的精确性及强相合性。此外，提出了一种新的计算高效的置信域椭球外包近似算法。新构造产生一个半定规划优化问题，其约束数量比向量化后直接应用椭球外包近似的约束数量低一个数量级。通过一系列数值实验亦经验性地验证了该方法的有效性。