Robustness of exponential stability of stochastic differential delay equations

Research output: Contribution to journalArticle

161 Citations (Scopus)

Abstract

Regard the stochastic differential delay equation dx(t) = [(A + Ā(t))x(t) + (B + B̄(t - τ))x(t - τ)] dt + g(t, x(t), x(t - τ)) dw(t) as the result of the effects of uncertainly, stochastic perturbation, and time lag to a linear ordinary differential equation ẋ(t) = (A + B)x(t). Assume the linear system is exponentially stable. In this paper we shall characterize how much the uncertainty, stochastic perturbation, and time lag the linear system can bear such that the stochastic delay system remains exponentially stable. The result will also be extended to nonlinear systems. 

LanguageEnglish
Pages442-447
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume41
Issue number3
DOIs
Publication statusPublished - 1996

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Asymptotic stability
Linear systems
Ordinary differential equations
Nonlinear systems
Uncertainty

Keywords

  • delay systems
  • linear systems
  • stability
  • stochastic systems
  • uncertain systems

Cite this

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Robustness of exponential stability of stochastic differential delay equations. / Mao, X.

In: IEEE Transactions on Automatic Control, Vol. 41, No. 3, 1996, p. 442-447.

Research output: Contribution to journalArticle

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KW - linear systems

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