Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems

Weiyin Fei, Liangjian Hu, Xuerong Mao, Mingxuan Shen

Research output: Contribution to journalArticle

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Abstract

Our recent paper [2] is the first to establish delay dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear we mean the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlin- ear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper [2]. We will then develop our ideas and methods there in order to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs.
Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalInternational Journal of Robust and Nonlinear Control
Publication statusAccepted/In press - 13 Oct 2018

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Stochastic Differential Delay Equations
Delay-dependent Stability
Stochastic systems
Hybrid Systems
Stochastic Systems
Growth Conditions
Stability criteria
Delay-dependent Criteria
Delay Equations
Coefficient
Stability Criteria
Linear Function
Continuation
Cover

Keywords

  • hybrid delay systems
  • Ito's formula
  • almost sure asymptotic stability
  • Lyapunov functional

Cite this

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Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems. / Fei, Weiyin; Hu, Liangjian; Mao, Xuerong; Shen, Mingxuan.

In: International Journal of Robust and Nonlinear Control , 13.10.2018, p. 1-18.

Research output: Contribution to journalArticle

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AU - Shen, Mingxuan

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AB - Our recent paper [2] is the first to establish delay dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear we mean the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlin- ear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper [2]. We will then develop our ideas and methods there in order to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs.

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KW - Ito's formula

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