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The Hadamard Product of Two Stable Multivariate Polynomials is not Necessarily Stable

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Abstract

In this note we demonstrate by a counterexample that the Hadamard product of two stable multivariate polynomials is not necessarily a stable multivariate polynomial.

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References

  1. J. Garloff and D.G. Wagner, “Hadamard Products of Stable Polynomials are Stable,” Journal of Mathematical Analysis and Applications, vol. 202, 1996, pp. 797–809.

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  2. V.L. Kharitonov and J.A. Torres Muñoz, “Robust Stability of Multivariate Polynomials Part 1: Small Coefficient Perturbations,” Multidimensional Systems and Signal Processing, vol. 10, 1999, pp. 7–20.

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  3. N.K. Bose, Applied Multidimensional Systems Theory, Van Nostrand Reinhold Company, 1982.

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Authors and Affiliations

  1. Automatic Control Department, CINVESTAV-IPN, Mexico, D.F., P.O. Box, 14-740, Mexico

    E. Rodríguez-Angeles, V. L. Kharitonov & J. A. Torres-Muñoz

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  1. E. Rodríguez-Angeles
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  2. V. L. Kharitonov
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  3. J. A. Torres-Muñoz
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Rodríguez-Angeles, E., Kharitonov, V.L. & Torres-Muñoz, J.A. The Hadamard Product of Two Stable Multivariate Polynomials is not Necessarily Stable. Multidimensional Systems and Signal Processing 15, 57–63 (2004). https://doi.org/10.1023/B:MULT.0000003932.21279.ea

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  • DOI: https://doi.org/10.1023/B:MULT.0000003932.21279.ea

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