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.