Characterization and Identification of Matrix Fraction Descriptions for LTI Systems
Characterization and Identification of Matrix Fraction Descriptions for LTI Systems
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DOI：
10.1137/14096832x
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
Biqiang Mu;Han-Fu Chen;L. Wang;G. Yin
中科院分区：
文献类型：
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作者：
Biqiang Mu;Han-Fu Chen;L. Wang;G. Yin
本文证明了线性定常系统的矩阵多项式$\{a (z)~B(z)\}$所给出的矩阵分式描述不一定是唯一的，即使$ a (z)$是一元的，$ a (z)$和$B(z)$没有公左因子，以及$ a (z)$和$B(z)$的最高阶项对应的矩阵系数是满行秩的。一个给定系统的所有可能的矩阵分数描述（mfd）的阶数是完全表征的。导出了确定矩阵对是否是系统的MFD的检验准则，该准则涉及由系统的脉冲响应或输出相关函数导出的某些Toeplitz矩阵的秩检验。设计了一个决策过程，为给定系统依次生成所有mfd。介绍了从输入输出数据或仅从输出数据估计给定系统的所有mfd的识别算法。然后将结果扩展到ARMAX系统。
This paper shows that the matrix fraction description, given by a pair $\{A(z)~B(z)\}$ of matrix polynomials of $z$, for a linear time-invariant system may not be unique even if $A(z)$ is monic, $A(z)$ and $B(z)$ have no common left factor, and the matrix coefficients corresponding to the highest-order terms of $A(z)$ and $B(z)$ are full row rank. The orders of all possible matrix fraction descriptions (MFDs) of a given system are completely characterized. Testing criteria for determining whether a matrix pair is an MFD of the system are derived, which involve rank tests of certain Toeplitz matrices derived from either the impulse response or output correlation functions of the system. A decision procedure is devised that generates sequentially all MFDs for a given system. Identification algorithms are introduced that estimate all MFDs of a given system from its input-output data or output data only. The results are then extended to cover ARMAX systems.