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

Wei Zhang, Linlin Ou, Xing He and Weidong Zhang

International Journal of Systems Science, 2015, vol. 46, issue 14, 2560-2571

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.

Date: 2015
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DOI: 10.1080/00207721.2013.873835

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