On stability of linear neutral differential equations in the Hale form

摘要

We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays (x(t)−a(t)x(g(t)))′=−b(t)x(h(t)),where |a(t)| < 1, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, in the case when the delays t−h(t), t−g(t) are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.