Geodesic
Stability Region for Discrete Time Systems and Its Boundary
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 246-255 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we investigate the Schur stability region of the $n$th 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 $n \geq 4$, 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.
Keywords: Schur stability, stability region, polytope, boundary set. 
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V. Dzhafarov; T. Büyükköroğlu; H. Akyar. Stability Region for Discrete Time Systems and Its Boundary. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 246-255. http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a19/

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