Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching

Hongliang Liu; Hui Wang; Guangren Duan

doi:10.1109/WCICA.2011.5970629

Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching

Hongliang Liu^*
, Hui Wang
, Guangren Duan

^*Corresponding author for this work

School of Astronautics

Harbin Normal University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.

Original language	English
Title of host publication	WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest
Pages	822-826
Number of pages	5
DOIs	https://doi.org/10.1109/WCICA.2011.5970629
State	Published - 2011
Event	2011 World Congress on Intelligent Control and Automation, WCICA 2011 - Taipei, Taiwan, Province of China Duration: 21 Jun 2011 → 25 Jun 2011

Publication series

Name	Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

Conference

Conference	2011 World Congress on Intelligent Control and Automation, WCICA 2011
Country/Territory	Taiwan, Province of China
City	Taipei
Period	21/06/11 → 25/06/11

Keywords

Brownian motion
Exponential stability
Generalized Ito's formula
Hybrid system
Markov chain

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10.1109/WCICA.2011.5970629

Cite this

Liu, H., Wang, H., & Duan, G. (2011). Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching. In WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest (pp. 822-826). Article 5970629 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA)). https://doi.org/10.1109/WCICA.2011.5970629

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title = "Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching",

abstract = "Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.",

keywords = "Brownian motion, Exponential stability, Generalized Ito's formula, Hybrid system, Markov chain",

author = "Hongliang Liu and Hui Wang and Guangren Duan",

year = "2011",

doi = "10.1109/WCICA.2011.5970629",

language = "英语",

isbn = "9781612847009",

series = "Proceedings of the World Congress on Intelligent Control and Automation (WCICA)",

pages = "822--826",

booktitle = "WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest",

note = "2011 World Congress on Intelligent Control and Automation, WCICA 2011 ; Conference date: 21-06-2011 Through 25-06-2011",

}

Liu, H, Wang, H & Duan, G 2011, Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching. in WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest., 5970629, Proceedings of the World Congress on Intelligent Control and Automation (WCICA), pp. 822-826, 2011 World Congress on Intelligent Control and Automation, WCICA 2011, Taipei, Taiwan, Province of China, 21/06/11. https://doi.org/10.1109/WCICA.2011.5970629

Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching. / Liu, Hongliang; Wang, Hui; Duan, Guangren.
WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest. 2011. p. 822-826 5970629 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA)).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching

AU - Liu, Hongliang

AU - Wang, Hui

AU - Duan, Guangren

PY - 2011

Y1 - 2011

N2 - Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.

AB - Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.

KW - Brownian motion

KW - Exponential stability

KW - Generalized Ito's formula

KW - Hybrid system

KW - Markov chain

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DO - 10.1109/WCICA.2011.5970629

M3 - 会议稿件

AN - SCOPUS:80052424625

SN - 9781612847009

T3 - Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

SP - 822

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BT - WCICA 2011 - 2011 World Congress on Intelligent Control and Automation, Conference Digest

T2 - 2011 World Congress on Intelligent Control and Automation, WCICA 2011

Y2 - 21 June 2011 through 25 June 2011

ER -

Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching

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