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The absolutely minimal realizations for first-degree nD SISO systems

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Abstract

Using partial fraction decomposition, limit methods and algebraic techniques, finding the absolutely minimal realization matrices for first-degree (multi-linear) nD SISO systems is transformed into solving a system of equations consisting of the all principal minors of an unknown matrix. Without using the symbolic approach by Gröbner basis, the necessary and sufficient conditions and construction of the absolutely minimal realizations for the degenerate and non-degenerate of transfer functions are derived. Five examples for first-degree 3D, 4D, and 5D SISO systems are presented to illustrate the basic ideas as well as the effectiveness of the proposed procedure, and computer programs written in Mathematica are also given.

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Acknowledgements

The author thanks the referees for their suggestions which have improved the original manuscript to the present version.

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  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China

    De-Yin Zheng

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Zheng, DY. The absolutely minimal realizations for first-degree nD SISO systems. Multidim Syst Sign Process 31, 345–366 (2020). https://doi.org/10.1007/s11045-019-00667-2

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