Stochastic stabilization and destabilization

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Abstract

It is shown in this paper that any nonlinear systems dot x(t) = f(x(t), t) in Rd can be stabilized by Brownian motion provided |f{hook}(x,t)| ≤ K|x| for some K > 0. On the other hand, this system can also be destabilized by Brownian motion if the dimension d ≥ 2. Similar results are also obtained for any given stochastic differential equation dx(t) = f{hook}(x(t), t) + g(x(t), t) dW(t).

Original languageEnglish
Pages (from-to)279-290
Number of pages12
JournalSystems and Control Letters
Volume23
Issue number4
DOIs
Publication statusPublished - 1994

Keywords

  • almost surely exponential stability
  • Brownian motion
  • nonlinear system
  • Stochastic stabilization and destabilization

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