Geodesic
On the real stability radius of a normal matrix
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 195-198 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A well-known formula expresses the real stability radius of a real $n$-by-$n$ matrix $A$ as the minimax of a certain function of two parameters: a complex parameter $\lambda$, which varies along the boundary of the stability region, and a real parameter $\gamma$, which varies on the interval $(0,1]$. It is shown that, for a normal matrix $A$ with a known spectrum $\sigma(A)=\{\lambda_1,\dots,\lambda_n\}$, the maximization with respect to $\gamma$ can be replaced by a finite computation involving the eigenvalues $\{\lambda_1,\dots,\lambda_n\}$. 
@article{ZVMMF_2005_45_2_a0,
     author = {Kh. D. Ikramov},
     title = {On the real stability radius of a~normal matrix},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {195--198},
     year = {2005},
     volume = {45},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a0/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - On the real stability radius of a normal matrix
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 195
EP  - 198
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a0/
LA  - ru
ID  - ZVMMF_2005_45_2_a0
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T On the real stability radius of a normal matrix
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 195-198
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a0/
%G ru
%F ZVMMF_2005_45_2_a0
Kh. D. Ikramov. On the real stability radius of a normal matrix. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 195-198. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a0/

[1] Doyle J. C., Stein G., “Multivariable feedback design: concepts for a classical/modern synthesis”, IEEE Trans. Automat. Control, 26 (1981), 4–16 | DOI | Zbl

[2] Chen M. J., Desoer C. A., “Necessary and sufficient condition for robust stability of linear distributed systems”, Internat. J. Control, 35 (1982), 255–267 | DOI | MR | Zbl

[3] Hinrichsen D., Pritchard A. J., “Stability radius for structured perturbations and the algebraic Riccati equation”, System. Control. Letts., 8 (1986), 105–113 | DOI | MR | Zbl

[4] Qiu L., Bernhardsson B., Rantzer A. et al., “A formula for computation of the real stability radius”, Automatica, 31:6 (1995), 879–890 | DOI | MR | Zbl