Stochastic stabilization and destabilization

Research output: Contribution to journalArticle

130 Citations (Scopus)

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).

LanguageEnglish
Pages279-290
Number of pages12
JournalSystems and Control Letters
Volume23
Issue number4
DOIs
Publication statusPublished - 1994

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Brownian movement
Stabilization
Nonlinear systems
Differential equations

Keywords

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

Cite this

@article{eddf20419651401cab4ed206eba6b39b,
title = "Stochastic stabilization and destabilization",
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).",
keywords = "almost surely exponential stability, Brownian motion, nonlinear system, Stochastic stabilization and destabilization",
author = "Xuerong Mao",
year = "1994",
doi = "10.1016/0167-6911(94)90050-7",
language = "English",
volume = "23",
pages = "279--290",
journal = "Systems and Control Letters",
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number = "4",

}

Stochastic stabilization and destabilization. / Mao, Xuerong.

In: Systems and Control Letters, Vol. 23, No. 4, 1994, p. 279-290.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stochastic stabilization and destabilization

AU - Mao, Xuerong

PY - 1994

Y1 - 1994

N2 - 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).

AB - 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).

KW - almost surely exponential stability

KW - Brownian motion

KW - nonlinear system

KW - Stochastic stabilization and destabilization

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U2 - 10.1016/0167-6911(94)90050-7

DO - 10.1016/0167-6911(94)90050-7

M3 - Article

VL - 23

SP - 279

EP - 290

JO - Systems and Control Letters

T2 - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 4

ER -