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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMM_2021_27_3_a19,
     author = {V. Dzhafarov and T. B\"uy\"ukk\"oro\u{g}lu and H. Akyar},
     title = {Stability {Region} for {Discrete} {Time} {Systems} and {Its} {Boundary}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {246--255},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a19/}
}
TY  - JOUR
AU  - V. Dzhafarov
AU  - T. Büyükköroğlu
AU  - H. Akyar
TI  - Stability Region for Discrete Time Systems and Its Boundary
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2021
SP  - 246
EP  - 255
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a19/
LA  - en
ID  - TIMM_2021_27_3_a19
ER  - 
%0 Journal Article
%A V. Dzhafarov
%A T. Büyükköroğlu
%A H. Akyar
%T Stability Region for Discrete Time Systems and Its Boundary
%J Trudy Instituta matematiki i mehaniki
%D 2021
%P 246-255
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a19/
%G en
%F TIMM_2021_27_3_a19
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/