Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations

In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential s...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 2; pp. 1758 - 1774
Main Author Liu, Kui
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
(ω，c)-periodic solutions
non-instantaneous impulsive differential equations
stability
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Summary:In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022101