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On the pole of non-square transfer function matrix Moore–Penrose pseudo-inverses

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  • Wei Zhang
  • Linlin Ou
  • Xing He
  • Weidong Zhang

Abstract

An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore–Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet–Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore–Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore–Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.

Suggested Citation

  • Wei Zhang & Linlin Ou & Xing He & Weidong Zhang, 2015. "On the pole of non-square transfer function matrix Moore–Penrose pseudo-inverses," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2560-2571, October.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:14:p:2560-2571
    DOI: 10.1080/00207721.2013.873835
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    References listed on IDEAS

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    1. Jieh-Shian Young, 2011. "Synthesis of decoupling controller for non-minimum phase plants of different pole numbers on RHP within uncertainties," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 939-950.
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