Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"
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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2010, Issue 3, Pages 33–37 (Mi vyurm189)  

Mathematics

Stability cone for the retarded linear matrix differential equation

T. N. Khokhlova

South Ural State University
References:
Abstract: Some surface in the three-dimensional space, named a stability cone is constructed. The necessary and sufficient condition of asymptotic stability of the matrix equation $\dot{x}(t)+Ax(t)+Bx(t-\tau)=0$ for random order matrixes which is connected with whether there are the auxiliary points which depend only on $A$ and $B$ matrix eigenvalues and on retardation value in a stability cone is proved. The matrixes $A$$B$ are required a joint triangulability.
Keywords: retorted differential equations, asymptotic stability, stability cone.
Received: 28.06.2010
Document Type: Article
UDC: 517.929
Language: Russian
Citation: T. N. Khokhlova, “Stability cone for the retarded linear matrix differential equation”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2010, no. 3, 33–37
Citation in format AMSBIB
\Bibitem{Kho10}
\by T.~N.~Khokhlova
\paper Stability cone for the retarded linear matrix differential equation
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2010
\issue 3
\pages 33--37
\mathnet{http://mi.mathnet.ru/vyurm189}
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