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.
- Bohl-perron theorem
- Explicit stability conditions
- Neutral equations in hale form
- Uniform exponential stability
- Variable delays
ASJC Scopus subject areas
- Mathematics (all)