EXPLICIT STABILITY TESTS FOR LINEAR NEUTRAL DELAY EQUATIONS USING INFINITE SERIES

摘要

We obtain new, explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays (x(t) - a(t)x(g(t)))' +b(t)x(h(t)) = 0, where vertical bar a(t)vertical bar <= A(0) <= 1, 0 <= b(0) <= b(t) <= B-0, 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 vertical bar a(t)vertical bar< 1/2 in known asymptotic stability tests and the consideration of variable delays.