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Article Dans Une Revue RAIRO - Theoretical Informatics and Applications (RAIRO: ITA) Année : 2007

Real and complex pseudozero sets for polynomials with applications

Résumé

Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero set and a comparison between these two pseudozero sets. We conclude that the complex pseudozero sets have to be preferred except when the perturbed real polynomials admit non-real zeros. We also give some applications of pseudozero set in control theory.
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Dates et versions

hal-01146488 , version 1 (25-10-2023)

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Stef Graillat, Philippe Langlois. Real and complex pseudozero sets for polynomials with applications. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2007, 41 (1), pp.45-56. ⟨10.1051/ita:2007006⟩. ⟨hal-01146488⟩
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