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Analysis of Noise under Regime Switching
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Abstract
In this paper we consider a stochastic nonlinear system under regime switching. Given a system <i>x(t)=f(x(t),r(t),t)</i> in which f satisfies so-called one-side polynomial growth condition. We introduce two Brownian noise feedbacks and stochastically perturb this system into <i>dx(t)=(x(t),r(t),t)dt+ σ (r(t))|x(t)|<sup>β</sup>x(t)dW<sub>1</sub>(t)+q(r(t))x(t)dW<sub>2</sub>(t)</i> . 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.
KeywordsHybrid SystemOne-Side Polynomial Growth ConditionIto FormulaStochastic Ultimate Boundedness
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