Article ID Journal Published Year Pages File Type
10414107 Systems & Control Letters 2005 13 Pages PDF
Abstract
In this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation. Given an unstable functional differential equation dx(t)/dt=f(t,xt), we stochastically perturb it into a stochastic functional differential equation dX(t)=f(t,Xt)dt+ΣX(t)dB(t), where Σ is a matrix and B(t) a Brownian motion while Xt={X(t+θ):-τ⩽θ⩽0}. Under the condition that f satisfies the local Lipschitz condition and obeys the one-side linear bound, we show that if the time lag τ is sufficiently small, there are many matrices Σ for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx(t)/dt=f(t,xt) may be unstable.
Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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