On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay

Wei Mao; Bo Chen; Fuke Wu; Xuerong Mao

doi:10.1016/j.sysconle.2023.105586

On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay

Wei Mao, Bo Chen, Fuke Wu, Xuerong Mao

Mathematics And Statistics

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2 Citations (Scopus)

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Abstract

This paper focuses on a class of hybrid stochastic delay systems with neutral term (HSDSwNT), where the time delay may be non-differentiable and the coefficients may not satisfy the linear growth condition. Under the local Lipschitz condition and the Khasminskii-type condition, the existence and uniqueness as well as boundedness of the solution to the HSDSwNT are established. By virtue of the Lyapunov function method and the M-matrix theory, sufficient conditions on the asymptotic stability and general decay stability are also examined for HSDSwNT. Finally, two examples are given to show the effectiveness of our results.

Original language	English
Article number	105586
Number of pages	27
Journal	Systems and Control Letters
Volume	178
Early online date	12 Jul 2023
DOIs	https://doi.org/10.1016/j.sysconle.2023.105586
Publication status	Published - 31 Aug 2023

Keywords

asymptotic stability
general decay stability
hybrid stochastic systems
neutral term
non-differentiable time delay

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10.1016/j.sysconle.2023.105586

Mao-etal-SCL-2023-On-the-existence-and-asymptotic-stability-of-hybridAccepted author manuscript, 904 KBLicence: CC BY-NC-ND 4.0

Long-time dynamics of numerical solutions of stochastic differential equations
Mao, X. (Principal Investigator)
Royal Society
1/10/16 → 30/09/21
Project: Research

Cite this

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title = "On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay",

abstract = "This paper focuses on a class of hybrid stochastic delay systems with neutral term (HSDSwNT), where the time delay may be non-differentiable and the coefficients may not satisfy the linear growth condition. Under the local Lipschitz condition and the Khasminskii-type condition, the existence and uniqueness as well as boundedness of the solution to the HSDSwNT are established. By virtue of the Lyapunov function method and the M-matrix theory, sufficient conditions on the asymptotic stability and general decay stability are also examined for HSDSwNT. Finally, two examples are given to show the effectiveness of our results.",

keywords = "asymptotic stability, general decay stability, hybrid stochastic systems, neutral term, non-differentiable time delay",

author = "Wei Mao and Bo Chen and Fuke Wu and Xuerong Mao",

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T1 - On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay

AU - Mao, Wei

AU - Chen, Bo

AU - Wu, Fuke

AU - Mao, Xuerong

PY - 2023/8/31

Y1 - 2023/8/31

N2 - This paper focuses on a class of hybrid stochastic delay systems with neutral term (HSDSwNT), where the time delay may be non-differentiable and the coefficients may not satisfy the linear growth condition. Under the local Lipschitz condition and the Khasminskii-type condition, the existence and uniqueness as well as boundedness of the solution to the HSDSwNT are established. By virtue of the Lyapunov function method and the M-matrix theory, sufficient conditions on the asymptotic stability and general decay stability are also examined for HSDSwNT. Finally, two examples are given to show the effectiveness of our results.

AB - This paper focuses on a class of hybrid stochastic delay systems with neutral term (HSDSwNT), where the time delay may be non-differentiable and the coefficients may not satisfy the linear growth condition. Under the local Lipschitz condition and the Khasminskii-type condition, the existence and uniqueness as well as boundedness of the solution to the HSDSwNT are established. By virtue of the Lyapunov function method and the M-matrix theory, sufficient conditions on the asymptotic stability and general decay stability are also examined for HSDSwNT. Finally, two examples are given to show the effectiveness of our results.

KW - asymptotic stability

KW - general decay stability

KW - hybrid stochastic systems

KW - neutral term

KW - non-differentiable time delay

U2 - 10.1016/j.sysconle.2023.105586

DO - 10.1016/j.sysconle.2023.105586

M3 - Article

SN - 0167-6911

VL - 178

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 105586

ER -

On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay

Abstract

Keywords

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Projects

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this