Hankel matrices for system identification

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Mu, Bi-Qiang¹  Chen, Han-Fu¹ 

[1] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Inst Syst Sci, Beijing 100190, Peoples R China

关键词: Hankel matrix;    Row-full-rank;    Impulse response;    Correlation function;    Multi-variable linear systems;   

DOI  :  10.1016/j.jmaa.2013.07.025

来源: Elsevier

【 摘 要 】

The coefficients of a linear system, even if it is a part of a block-oriented nonlinear system, normally satisfy some linear algebraic equations via Hankel matrices composed of impulse responses or correlation functions. In order to determine or to estimate the coefficients of a linear system it is important to require the associated Hankel matrix be of row-full-rank. The paper first discusses the equivalent conditions for identifiability of the system. Then, it is shown that the row-full-rank of the Hankel matrix composed of impulse responses is equivalent to identifiability of the system. Finally, for the row-full-rank of the Hankel matrix composed of correlation functions, the necessary and sufficient conditions are presented, which appear slightly stronger than the identifiability condition. In comparison with existing results, here the minimum phase condition is no longer required for the case where the dimension of the system input and output is the same, though the paper does not make such a dimensional restriction. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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