Geodesic
Stability cone for the retarded linear matrix differential equation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 3 (2010), pp. 33-37

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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. 
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     author = {T. N. Khokhlova},
     title = {Stability cone for the retarded linear matrix differential equation},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {33--37},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2010_3_a4/}
}
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T. N. Khokhlova. Stability cone for the retarded linear matrix differential equation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 3 (2010), pp. 33-37. http://geodesic.mathdoc.fr/item/VYURM_2010_3_a4/