Explicit stability tests for linear neutral delay equations using\n infinite series

2019/04/29 by Leonid Berezansky, Berezansky, Leonid, Elena Braverman +1
Materials Science · #34K06 #34K20 #34K40 #Dynamical Systems (math.DS) #FOS: Mathematics #Synthesis and properties of polymers

paper · pdf · doi:10.48550/arxiv.1904.12849

openalex publication_date 2019/04/29 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We obtain new explicit exponential stability conditions for the linear scalar\nneutral equation with two bounded delays (x(t)-a(t)x(g(t)))'+b(t)x(h(t))=0, \nwhere |a(t)| \≤ A₀ < 1, 0<b₀\≤ b(t)\≤ B₀, assuming that all\nparameters of the equation are measurable functions.\n To analyze exponential stability, we apply the Bohl-Perron theorem and a\nreduction of a neutral equation to an equation with an infinite number of\nnon-neutral delay terms. This method has never been used before for this\nneutral equation; its application allowed to omit a usual restriction\n|a(t)|<\(1)/(2) in known asymptotic stability tests and consider variable\ndelays.\n

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