Abstract:
In this paper we investigate the Schur stability region of the nth order polynomials in the coefficient space. Parametric description of the boundary set is obtained. We show that all the boundary can be obtained as a multilinear image of three (n−1)-dimensional boxes. For even and odd n these boundary boxes are different. Analogous properties for the classical multilinear reflection map are unknown. It is shown that for n≥4, both two parts of the boundary which are pieces of the corresponding hyperplanes are nonconvex. Polytopes in the nonconvex stability region are constructed. A number of examples are provided.
Citation:
V. Dzhafarov, T. Büyükköroğlu, H. Akyar, “Stability Region for Discrete Time Systems and Its Boundary”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 246–255
\Bibitem{DzhBuyAky21}
\by V.~Dzhafarov, T.~B\"uy\"ukk\"oro{\u g}lu, H.~Akyar
\paper Stability Region for Discrete Time Systems and Its Boundary
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 246--255
\mathnet{http://mi.mathnet.ru/timm1853}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-3-246-255}
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\elib{https://elibrary.ru/item.asp?id=46502705}
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https://www.mathnet.ru/eng/timm1853
https://www.mathnet.ru/eng/timm/v27/i3/p246
This publication is cited in the following 1 articles:
Şerife YILMAZ, “Robust Stability and Stable Member Problems for Multilinear Systems”, Cumhuriyet Science Journal, 43:3 (2022), 492
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