Stochastic stabilization and destabilization

Xuerong Mao

doi:10.1016/0167-6911(94)90050-7

Stochastic stabilization and destabilization

Xuerong Mao^*

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

201 Citations (Scopus)

Abstract

It is shown in this paper that any nonlinear systems dot x(t) = f(x(t), t) in R^d 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 language	English
Pages (from-to)	279-290
Number of pages	12
Journal	Systems and Control Letters
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/0167-6911(94)90050-7
Publication status	Published - 1994

Keywords

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

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10.1016/0167-6911(94)90050-7

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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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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

UR - http://www.scopus.com/inward/record.url?scp=0028518403&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0028518403

SN - 0167-6911

VL - 23

SP - 279

EP - 290

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 4

ER -

Stochastic stabilization and destabilization

Abstract

Keywords

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