Explicit conditions of exponential stability for a linear impulsive delay differential equation

L. Berezansky; E. Braverman

doi:10.1006/jmaa.1997.5578

Explicit conditions of exponential stability for a linear impulsive delay differential equation

L. Berezansky
, E. Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

For a scalar delay differential equation x(t) + ∑^m_{k = 1} A_k(t)x[h_k(t)] = 0, t ε [0, ∞), x(t) ε R, h_k(t) ≤ t, with impulsive conditions x(τ_j) = B_jx(τ_j - 0), 1im_j→∞ τ_j = ∞ explicit exponential stability results are obtained.

Original language	English
Pages (from-to)	439-458
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	214
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1997.5578
State	Published - 15 Oct 1997

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.1997.5578

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@article{46dc9971c6694a6d8badb363fce7871e,

title = "Explicit conditions of exponential stability for a linear impulsive delay differential equation",

abstract = "For a scalar delay differential equation x(t) + ∑mk = 1 Ak(t)x[hk(t)] = 0, t ε [0, ∞), x(t) ε R, hk(t) ≤ t, with impulsive conditions x(τj) = Bjx(τj - 0), 1imj→∞ τj = ∞ explicit exponential stability results are obtained.",

author = "L. Berezansky and E. Braverman",

year = "1997",

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doi = "10.1006/jmaa.1997.5578",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Explicit conditions of exponential stability for a linear impulsive delay differential equation

AU - Berezansky, L.

AU - Braverman, E.

PY - 1997/10/15

Y1 - 1997/10/15

N2 - For a scalar delay differential equation x(t) + ∑mk = 1 Ak(t)x[hk(t)] = 0, t ε [0, ∞), x(t) ε R, hk(t) ≤ t, with impulsive conditions x(τj) = Bjx(τj - 0), 1imj→∞ τj = ∞ explicit exponential stability results are obtained.

AB - For a scalar delay differential equation x(t) + ∑mk = 1 Ak(t)x[hk(t)] = 0, t ε [0, ∞), x(t) ε R, hk(t) ≤ t, with impulsive conditions x(τj) = Bjx(τj - 0), 1imj→∞ τj = ∞ explicit exponential stability results are obtained.

UR - https://www.scopus.com/pages/publications/0031251139

U2 - 10.1006/jmaa.1997.5578

DO - 10.1006/jmaa.1997.5578

M3 - Article

AN - SCOPUS:0031251139

SN - 0022-247X

VL - 214

SP - 439

EP - 458

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Explicit conditions of exponential stability for a linear impulsive delay differential equation

Abstract

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