Geodesic
On different types of stability of linear polytopic systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 272-280

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Different types of stability of linear uncertain systems are considered. Stability conditions in terms of nonsingularity are obtained. Numerical examples of using the Bernstein expansion of the determinant function are given.
Keywords: linear systems, stability, Bernstein expansion. 
V. Dzhafarov; T. Büyükköroğlu; Ö. Esen. On different types of stability of linear polytopic systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 272-280. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a20/
@article{TIMM_2010_16_1_a20,
     author = {V. Dzhafarov and T. B\"uy\"ukk\"oro\u{g}lu and \"O. Esen},
     title = {On different types of stability of linear polytopic systems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {272--280},
     year = {2010},
     volume = {16},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a20/}
}
TY  - JOUR
AU  - V. Dzhafarov
AU  - T. Büyükköroğlu
AU  - Ö. Esen
TI  - On different types of stability of linear polytopic systems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 272
EP  - 280
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a20/
LA  - en
ID  - TIMM_2010_16_1_a20
ER  - 
%0 Journal Article
%A V. Dzhafarov
%A T. Büyükköroğlu
%A Ö. Esen
%T On different types of stability of linear polytopic systems
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 272-280
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a20/
%G en
%F TIMM_2010_16_1_a20

[1] Krasovskii N. N., Control Theory of Motion, Nauka, Moscow, 1968, 475 pp. | MR

[2] Wonham W. M., Linear multivariable control: a geometric approach, 2nd ed., Springer-Verlag, New York, 1979, 326 pp. | MR | Zbl

[3] Luenberger D. G., “Observers for multivariable systems”, IEEE Transactions on Automatic Control, AC-11 (1966), 190–197 | DOI

[4] Dzhafarov V., Büyükköroǧlu T., “On nonsingularity of a polytope of matrices”, Linear Algebra and Its Appl., 429:5–6 (2008), 1174–1183 | DOI | MR | Zbl

[5] Garloff J., “The Bernstein algorithm”, Interval Computations, 2 (1993), 154–168 | MR | Zbl

[6] Zettler M., Garloff J., “Robustness analysis of polynomials with polynomial parameter dependency using Bernstein expansion”, IEEE Trans. Automatic. Control., 43:3 (1998), 425–431 | DOI | MR | Zbl