Exponential Stability Tests for Linear Delayed Differential Systems Depending on All Delays

Linear delayed differential systems $$\begin{aligned} \dot{x}_i(t)=\sum _{j=1}^m \sum _{k=1}^{r_{ij}}a_{ij}^{k}(t)x_j\left( h_{ij}^{k}(t)\right) ,\quad i=1,\dots ,m \end{aligned}$$are considered on a half-infinity interval $$t\ge 0$$. It is assumed that m and $$r_{ij}$$, $$i,j=1,\dots ,m$$ are natural numbers and the coefficients $$a_{ij}^{k}:[0,\infty )\rightarrow \mathbb {R}$$ and delays $$h_{ij}^{k}:[0,\infty )\rightarrow {\mathbb {R}}$$ are Lebesgue measurable functions. New explicit results on uniform exponential stability, depending on all delays, are derived. The conditions obtained do not require the dominance of diagonal terms over the off-diagonal terms as most of the existing stability tests for non-autonomous delay differential systems do.