Various results and techniques, such as Bohl-Perron theorem, a priori solution estimates, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations $$ \dot{ x_i}(t)=A_i(t)x_i(h_i(t)) +\sum_{ j=1}^n \sum_{ k=1}^{ m_{ ij}} B_{ ij}^k(t)x_j(h_{ ij}^k(t)) + \sum_{ j=1}^n\int\limits_{ g_{ ij}(t)}^t K_{ ij}(t,s)x_j(s)ds,~i=1,\dots,n. $$ Here $x_i$ are unknown vector functions, $A_i, B_{ ij}^k, K_{ ij}$ are matrix functions, $h_i,h_{ ij}^k, g_{ ij}$ are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.
Categories: math.DS