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JOURNALS // Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika" // Archive

Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 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

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.

UDC: 517.929

Received: 28.06.2010



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