On the determination of the Smith-McMillan form of a rational matrix from its Laurent expansion
(1979) IEEE Transactions on Circuits and Systems — Vol. 26, n° 3, p. 180-189 (1979)
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- Abstract
- A novel method is presented to determine the SmithMacmillan form of a rationalm times nmatrixR(p)from Laurent expansions in its poles and zeros. Based on that method, a numerically stable algorithm is deduced, which uses only a minimal number of terms of the Laurent expansion, hence providing a shortcut with respect to cumbersome and unstable procedures based on elementary transformations with unimodular matrices. The method can be viewed as a generalization of Kublanovkaya's algorithm for the complete solution of the eigenstructre problem forlambda I - A. From a system's point of view it provides a handy and numerically stable way to determine the degree of a zero of a transfer function and unifies a number of results from multivariable realization and invertibility theory. The paper presents a systematic treatment of the relation between the eigen-information of a transfer function and the information contained in partial fraction or Laurent expansions. Although a number of results are known, they are presented in a systematic way which considerably simplifies the total picture and introduces in a natural way a number of novel techniques.
- Affiliations
KULeuven EE Dept
Citations
Van Dooren, P., Dewilde, P., & Vandewalle, J. (1979). On the determination of the Smith-McMillan form of a rational matrix from its Laurent expansion. IEEE Transactions on Circuits and Systems, 26(3), 180-189. https://doi.org/10.1109/TCS.1979.1084628 (Original work published 1979)