Approximating characteristic equations for autonomous systems of differential equations with aftereffect (Q646837)

The linear autonomous system of differential equations with aftereffect \[ x'(t) = \int_{-\tau}^0 d\eta(\theta) x(t+\theta)\;,\quad t\in (0,\infty)\;, \] where \(x:[-\tau,\infty)\to\mathbb R^n\), and \(\eta\) is a matrix function with bounded variation on \([-\tau,0]\) and \(\eta(0)=0\), is considered. Some asymptotic formulae are established.