An extended inner-outer factorisation algorithm based on the structure of a transfer function matrix inverse

In this paper, the structure feature of the inverse of a multi-input/multi-output square transfer function matrix is explored. Instead of complicated advanced mathematical tools, we only use basic results of complex analysis in the analysing procedure. By employing the Laurent expression, an elegant...

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Bibliographic Details
Published in:International journal of systems science Vol. 47; no. 7; pp. 1624 - 1635
Main Authors: Zhang, Wei, Zhao, Chunhui, He, Xing, Zhang, Weidong
Format: Journal Article
Language:English
Published: Taylor & Francis 18.05.2016
Subjects:
Algorithms
Approximation
complex analysis
Computation
inner-outer factorisation
Inverse
Laurent expansion
Mathematical analysis
Mathematical models
standard series expansion
transfer function matrix inverse
Transfer functions
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:In this paper, the structure feature of the inverse of a multi-input/multi-output square transfer function matrix is explored. Instead of complicated advanced mathematical tools, we only use basic results of complex analysis in the analysing procedure. By employing the Laurent expression, an elegant structure form of the expansion is obtained for the transfer function matrix inverse. This expansion form is the key of deriving an analytical solution to the inner-outer factorisation for both stable plants and unstable plants. Different from other computation algorithm, the obtained inner-outer factorisation is given in an analytical form. The solution is exact and without approximation. Numerical examples are provided to verify the correctness of the obtained results.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2014.942244