Scalar criteria for exponential stability of functional differential equations

Ngoc, Pham Huu Anh; Tran, Thai Bao; Tinh, Cao Thanh; Huy, Nguyen Dinh

doi:10.1016/j.sysconle.2020.104642

Cited by 5 publications

(2 citation statements)

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“…This latter requirement is stronger than either (H4) or (H5). More recently, Ngoc et al [29] considered linear DDEs (3.1) but only with finite delay, without requiring a priori uniforms bounds of all the coefficients; for the situation of finite delay, Theorem 3.2. (iv) in [29] is exactly the criterion expressed in our Theorem 3.1.…”

Section: Proof As Described Above After Rescaling the Variables By XImentioning

confidence: 99%

“…For the last few years, there has been a renewed interest in the analysis of stability of nonautonomous linear DDEs, and several methods and tools have been proposed, see e.g. [2,4,5,14,15,17,18,21,28,29] and references therein. The main goal of this paper is to obtain new explicit sufficient conditions for the asymptotic and exponential asymptotic stability of a general linear system (1.1), which improve and generalize some criteria in recent literature.…”

Section: Introductionmentioning

confidence: 99%

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Stability for nonautonomous linear differential systems with infinite delay

Faria

2020

Preprint

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We study the stability of general n-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first situation, the effect of the delays is dominated by nondelayed diagonal negative feedback terms, and sufficient conditions for both the asymptotic and the exponential asymptotic stability of the system are given. In the second case, the stability depends on the size of some bounded diagonal delays and coefficients, although terms with unbounded delay may co-exist. Our results encompass DDEs with discrete and distributed delays, and enhance some recent achievements in the literature.

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Section: Proof As Described Above After Rescaling the Variables By XImentioning

confidence: 99%