Stochastic suppression and stabilization of functional differential equations

Fuke Wu, Xuerong Mao, Shigeng Hu

Research output: Contribution to journalArticleResearchpeer-review

25 Citations (Scopus)


Without the linear growth condition or the one-sided linear growth condition, this paper discusses whether or not stochastic noise feedback can stabilize a given unstable nonlinear functional system (x)over dot(t) = f(x(t), t). Since f may defy the linear growth condition or the onesided linear growth condition, this system may explode in a finite time. To stabilize this system, this paper stochastically perturbs this system into the stochastic functional differential system dx(t) = f (x(t), t)dt + qx(t)dw(1)(t)+sigma vertical bar x(t)vertical bar(beta)x(t)dw(2)(t) by two independent Brownian motions w(1)(t) and w(2)(t). This paper shows that the Brownian motion w(2)(t) may suppress the potential explosion of the solution for appropriate beta. Moreover, for sufficiently large q, this stochastic functional system is exponentially stable. These results can be used to examine stochastic stabilization.
Original languageEnglish
Pages (from-to)745 - 753
Number of pages9
JournalSystems and Control Letters
Issue number12
Publication statusPublished - 2010
Externally publishedYes

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