I want to analyze the stability of a distributed delayed differential equations that look like,
$$\dot x(t)=a x(t)+b \int_0^\infty x(t-s) g(s) ds $$,
where $a$ and $b$ are constants and $g(s)$ is a continuous kernel with $g(s) \in L^1$.
Suppose $x(t)$ has a steady state, $x=\bar x$.
How do I find the characteristic equation of this equation? In which cases it is asymptotically stable?