Explicit stability tests for linear neutral delay equations using infinite series

We obtain new, explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays (x(t) − a(t)x(g(t)))⁰ + b(t)x(h(t)) = 0, where |a(t)| ≤ A₀ < 1, 0 < b₀ ≤ b(t) ≤ B₀, assuming that all parameters of the equation are measurable functions. To analyze the exponential stability, we apply the Bohl-Perron theorem and a reduction of a neutral equation to an equation with an infinite number of non-neutral delay terms. This method has never before been used for this neutral equation; its application allows omitting a usual restriction |a(t)| < 1/2 in known asymptotic stability tests and the consideration of variable delays.