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.