On exponential stability of hybrid neutral stochastic differential delay equations with different structures

A. Wu; Surong You; Wei Mao; Xuerong Mao; Liangjian Hu

On exponential stability of hybrid neutral stochastic differential delay equations with different structures

A. Wu, Surong You, Wei Mao, Xuerong Mao, Liangjian Hu

Mathematics And Statistics

Research output: Contribution to journal › Article

Abstract

This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and proved

Original language	English
Journal	Nonlinear Analysis: Hybrid Systems
Publication status	Accepted/In press - 15 Sep 2020

Keywords

M-matrix
exponential stability
hybrid neutral stochastic differential delay equation
Lyapunov function
Khasminskii-type condition

Access to Document

https://www.sciencedirect.com/journal/nonlinear-analysis-hybrid-systems

Embargoed Document

Wu-etal-NAHS-2020-On-exponential-stability-of-hybrid-neutral-stochastic-differential-delay-equations-with-different-structures
Accepted author manuscript, 520 KB
Licence: CC BY-NC-ND 4.0
Embargo ends: 15/09/21

Fingerprint Dive into the research topics of 'On exponential stability of hybrid neutral stochastic differential delay equations with different structures'. Together they form a unique fingerprint.

Projects

1 Finished
1 Active

Long-time dynamics of numerical solutions of stochastic differential equations

Mao, X.

Royal Society

1/10/16 → 30/09/21

Project: Research

Numerical Analysis of Stochastic Differential Equations: New Challenges

Mao, X.

Leverhulme Trust

1/10/15 → 30/09/17

Project: Research Fellowship

Cite this

Wu, A., You, S., Mao, W., Mao, X., & Hu, L. (Accepted/In press). On exponential stability of hybrid neutral stochastic differential delay equations with different structures. Nonlinear Analysis: Hybrid Systems.

@article{2d3d9744ee3b48ceae3a7b25ca56ad40,

title = "On exponential stability of hybrid neutral stochastic differential delay equations with different structures",

abstract = "This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and proved",

keywords = "M-matrix, exponential stability, hybrid neutral stochastic differential delay equation, Lyapunov function, Khasminskii-type condition",

author = "A. Wu and Surong You and Wei Mao and Xuerong Mao and Liangjian Hu",

year = "2020",

month = sep,

day = "15",

language = "English",

journal = "Nonlinear Analysis: Hybrid Systems",

issn = "1751-570X",

}

TY - JOUR

T1 - On exponential stability of hybrid neutral stochastic differential delay equations with different structures

AU - Wu, A.

AU - You, Surong

AU - Mao, Wei

AU - Mao, Xuerong

AU - Hu, Liangjian

PY - 2020/9/15

Y1 - 2020/9/15

N2 - This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and proved

AB - This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and proved

KW - M-matrix

KW - exponential stability

KW - hybrid neutral stochastic differential delay equation

KW - Lyapunov function

KW - Khasminskii-type condition

UR - https://www.sciencedirect.com/journal/nonlinear-analysis-hybrid-systems

M3 - Article

JO - Nonlinear Analysis: Hybrid Systems

JF - Nonlinear Analysis: Hybrid Systems

SN - 1751-570X

ER -