TY - JOUR

T1 - Explicit stability tests for linear neutral delay equations using infinite series

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information:
2010 AMS Mathematics subject classification. Primary 34K06, 34K20, 34K40. Keywords and phrases. Neutral equations in Hale form, uniform exponential stability, Bohl-Perron theorem, variable delays, explicit stability conditions. This research was partially supported by NSERC, grant No. RGPIN-2015-05976. Received by the editors on July 8, 2018, and in revised form on September 6, 2018.
Publisher Copyright:
Copyright © 2019 Rocky Mountain Mathematics Consortium.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Bohl-perron theorem

KW - Explicit stability conditions

KW - Neutral equations in hale form

KW - Uniform exponential stability

KW - Variable delays

UR - http://www.scopus.com/inward/record.url?scp=85068979673&partnerID=8YFLogxK

U2 - 10.1216/RMJ-2019-49-2-387

DO - 10.1216/RMJ-2019-49-2-387

M3 - Article

AN - SCOPUS:85068979673

VL - 49

SP - 387

EP - 403

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 2

ER -