Geodesic
On the real stability radius of a normal matrix
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 195-198

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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 $\{\lambda_1,\dots,\lambda_n\}$. 
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     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},
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     number = {2},
     year = {2005},
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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/