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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2010, Issue 3, Pages 33–37
(Mi vyurm189)
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Mathematics
Stability cone for the retarded linear matrix differential equation
T. N. Khokhlova South Ural State University
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
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
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https://www.mathnet.ru/eng/vyurm189 https://www.mathnet.ru/eng/vyurm/y2010/i3/p33
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Abstract page: | 82 | Full-text PDF : | 43 | References: | 24 |
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