Delay dependent stability of highly nonlinear hybrid stochastic systems

Weiyin Fei, Liangjian Hu, Xuerong Mao, Mingxuan Shen

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)
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There are lots of papers on the delay dependent stability criteria for differential delay equations (DDEs), stochastic differential delay equations (SDDEs) and hybrid SDDEs. A common feature of these existing criteria is that they can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions (namely, satisfy the linear growth condition). In other words, there is so far no delay-dependent stability criterion on nonlinear equations without the linear growth condition (we will refer to such equations as highly nonlinear ones). This paper is the first to establish delay dependent criteria for highly nonlinear hybrid SDDEs. It is therefore a breakthrough in the stability study of highly nonlinear hybrid SDDEs
Original languageEnglish
Pages (from-to)165-170
Number of pages6
Early online date18 May 2017
Publication statusE-pub ahead of print - 18 May 2017


  • H∞ stability
  • hybrid delay systems
  • asymptotic stability
  • Lyapunov functional
  • delay-dependent stability criterion
  • nonlinear equations
  • time-delay
  • differential delay equations


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