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arXiv · 2310.11790

Finite Sample Performance Analysis of MIMO Systems Identification

Shuai Sun·Jiayun Li·Yilin Mo
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Abstract

This paper is concerned with the finite sample identification performance of an n dimensional discrete-time Multiple-Input Multiple-Output (MIMO) Linear Time-Invariant system, with p inputs and m outputs. We prove that the widely-used Ho-Kalman algorithm and Multivariable Output Error State Space (MOESP) algorithm are ill-conditioned for MIMO systems when n/m or n/p is large. Moreover, by analyzing the Cra\'mer-Rao bound, we derive a fundamental limit for identifying the real and stable (or marginally stable) poles of MIMO system and prove that the sample complexity for any unbiased pole estimation algorithm to reach a certain level of accuracy explodes superpolynomially with respect to n/(pm). Numerical results are provided to illustrate the ill-conditionedness of Ho-Kalman algorithm and MOESP algorithm as well as the fundamental limit on identification.

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Shuai Sun, Jiayun Li, Yilin Mo. 2023-10-18. Finite Sample Performance Analysis of MIMO Systems Identification. https://arxiv.org/abs/2310.11790

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