The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise

Wei  Mao; Liangjian Hu; Xuerong Mao

doi:10.1016/j.jfranklin.2019.11.068

The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise

Wei Mao, Liangjian Hu, Xuerong Mao

Mathematics And Statistics

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Abstract

The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the local Lipschitz condition and non-linear growth condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results.

Original language	English
Pages (from-to)	1174-1198
Number of pages	25
Journal	Journal of the Franklin Institute
Volume	357
Issue number	2
Early online date	5 Dec 2019
DOIs	https://doi.org/10.1016/j.jfranklin.2019.11.068
Publication status	Published - 31 Jan 2020

Keywords

hybrid stochastic systems
pantograph delay
non-Gaussian Lévy noise
asymptotic stability
polynomial stability

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10.1016/j.jfranklin.2019.11.068

Mao-etal-JFI-2019-The-asymptotic-stability-of-hybrid-stochastic-systems-with-pantograph-delayAccepted author manuscript, 164 KBLicence: CC BY-NC-ND 4.0

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title = "The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian L{\'e}vy noise",

abstract = "The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian L{\'e}vy noise (HSSwPDLNs). Under the local Lipschitz condition and non-linear growth condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results.",

keywords = "hybrid stochastic systems, pantograph delay, non-Gaussian L{\'e}vy noise, asymptotic stability, polynomial stability",

author = "Wei Mao and Liangjian Hu and Xuerong Mao",

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T1 - The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise

AU - Mao, Wei

AU - Hu, Liangjian

AU - Mao, Xuerong

PY - 2020/1/31

Y1 - 2020/1/31

N2 - The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the local Lipschitz condition and non-linear growth condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results.

AB - The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the local Lipschitz condition and non-linear growth condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results.

KW - hybrid stochastic systems

KW - pantograph delay

KW - non-Gaussian Lévy noise

KW - asymptotic stability

KW - polynomial stability

UR - https://www.journals.elsevier.com/journal-of-the-franklin-institute/

U2 - 10.1016/j.jfranklin.2019.11.068

DO - 10.1016/j.jfranklin.2019.11.068

M3 - Article

SN - 0016-0032

VL - 357

SP - 1174

EP - 1198

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 2

ER -

The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise

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