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J. A. D. Appleby, X. R. Mao and A. Rodkina, “Stabilization and Destabilization of Nonlinear Differential Equations by Noise,” IEEE Transactions on Automatic Control, Vol. 53, No. 3, 2008, pp. 683-691. doi:10.1109/TAC.2008.919255

has been cited by the following article:

• TITLE: Analysis of Noise under Regime Switching

  AUTHORS: Ling Bai, Xiaoyue Li

  KEYWORDS: Hybrid System, One-Side Polynomial Growth Condition, Ito Formula, Stochastic Ultimate Boundedness

  JOURNAL NAME: Applied Mathematics, Vol.2 No.7, July 6, 2011

  ABSTRACT: In this paper we consider a stochastic nonlinear system under regime switching. Given a system x(t)=f(x(t),r(t),t) in which f satisfies so-called one-side polynomial growth condition. We introduce two Brownian noise feedbacks and stochastically perturb this system into dx(t)=(x(t),r(t),t)dt+ σ (r(t))|x(t)|βx(t)dW1(t)+q(r(t))x(t)dW2(t) . It can be proved that appropriate noise intensity may suppress the potentially explode in a finite time and ensure that this system is almost surely exponentially stable although the corresponding system without Brownian noise perturbation may be unstable system.