Investigation of the global positivity of polynomials via linear optimization

Tibken, Bernd; Dilaver, Kamil Fatih; Schwenk, Sebastian

doi:10.1109/nds.2005.195333

Cited by 2 publications

(1 citation statement)

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“…This section will closely follow the corresponding section in (Ehlich and Zeller, 1964;Tibken and Dilaver, 2004;Tibken et al, 1999). In the following J = [a, b] denotes a nonempty compact real interval with J ⊂ R. The set of Chebychev points in J is defined for a given natural number N > 0 by…”

Section: Theorem Of Ehlich and Zellermentioning

confidence: 73%

Investigation of Parameter Perturbation Region for Positive Polynomials

Tibken

Dilaver

2005

IFAC Proceedings Volumes

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In this paper the robust positivity of polynomials under coefficient perturbation is investigated. This robust positivity of polynomials can be used for polynomial systems in order to determine the robust asymptotic stability of the system. It is assumed that the polynomials under investigation depend linearly on some parameters. The aim in the article is to determine the parameter perturbation region as a hypersphere, for which the polynomial is globally positive. The theorem of Ehlich and Zeller is used to achieve this aim. This theorem enables to give conditions in the parameter space for global positivity. These conditions are linear inequalities. By means of these inequalities an inner and an outer approximation are calculated to the relevant perturbation region which is a hypersphere. Two nontrivial examples conclude the paper and show the effectiveness of the presented method.

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Section: Theorem Of Ehlich and Zellermentioning

confidence: 73%