Approximate determination of the stability domain of a linear delay differential equation with periodic coefficient (Q2461915)

Consider the scalar linear delay differential equation \[ \dot x(t)= a(t) x(t)- bx(t-1),\tag{\(*\)} \] where \(a\) is periodic and \(b\) is a constant. The author sketches an approach to approximate the stability domain of the equilibrium \(x(t)\equiv 0\) of \((*)\) by studying the fixed point of a finite-dimensional map.