Stability of hybrid stochastic retarded systems

Lirong Huang, Xuerong Mao, Feiqi Deng

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used.
LanguageEnglish
Pages3413-3420
Number of pages7
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Volume55
Issue number11
DOIs
Publication statusPublished - 2008

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Asymptotic stability
Large scale systems
Differential equations

Keywords

  • asymptotic stability
  • markov chain
  • razumikhintypetheorems
  • retarded systems
  • stochastic systems

Cite this

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Stability of hybrid stochastic retarded systems. / Huang, Lirong; Mao, Xuerong; Deng, Feiqi.

In: IEEE Transactions on Circuits and Systems I: Regular Papers , Vol. 55, No. 11, 2008, p. 3413-3420.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stability of hybrid stochastic retarded systems

AU - Huang, Lirong

AU - Mao, Xuerong

AU - Deng, Feiqi

PY - 2008

Y1 - 2008

N2 - Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used.

AB - Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used.

KW - asymptotic stability

KW - markov chain

KW - razumikhintypetheorems

KW - retarded systems

KW - stochastic systems

U2 - 10.1109/TCSI.2008.2001825

DO - 10.1109/TCSI.2008.2001825

M3 - Article

VL - 55

SP - 3413

EP - 3420

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

T2 - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

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