Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay

Yangzi Hu, Fuke Wu, Chengming Huang

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)

Abstract

We regard the stochastic functional differential equation with infinite delay dx(t) = f(x(t))dt +g(x(t))dw(t) as the result of the effects of stochastic perturbation to the deterministic functional differential equation (x) over dot (t) = f (x(t)), where x(t) = X(t) (theta) is an element of C((-infinity, 0]; R(n)) is defined by x(t) (theta) = x(t + theta), theta is an element of (-infinity, 0]. We assume that the deterministic system with infinite delay is exponentially stable. In this paper, we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable.
Original languageEnglish
Pages (from-to)2577 - 2584
Number of pages8
JournalAutomatica
Volume45
Issue number11
DOIs
Publication statusPublished - 2009
Externally publishedYes

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