Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise

Nishanth Lingala; N. Sri Namachchivaya; Oliver M. O'Reilly; Volker Wihstutz

doi:10.1016/j.probengmech.2012.12.008

Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise

Nishanth Lingala, N. Sri Namachchivaya, Oliver M. O'Reilly, Volker Wihstutz

Aerospace Engineering

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

Abstract

An oscillator of the form q̇(t)+2ζq̇(t)+q(t)=-κ[q(t)- q(t-r)] is unstable when the strength of the feedback (κ) is greater than a critical value (^κc). Oscillations of constant amplitude persist when κ=^κc. We study the almost-sure asymptotic stability of the oscillator when κ=^κc and the system is excited by a two-state Markov noise. For small intensity noise, we construct an asymptotic expansion for the maximal Lyapunov exponent.

Original language	English (US)
Pages (from-to)	21-30
Number of pages	10
Journal	Probabilistic Engineering Mechanics
Volume	32
DOIs	https://doi.org/10.1016/j.probengmech.2012.12.008
State	Published - 2013

Keywords

Almost-sure stability
Chatter
Delay differential equation
Lyapunov exponent

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Civil and Structural Engineering
Nuclear Energy and Engineering
Condensed Matter Physics
Aerospace Engineering
Ocean Engineering
Mechanical Engineering

Online availability

10.1016/j.probengmech.2012.12.008

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title = "Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise",

abstract = "An oscillator of the form {\.q}(t)+2ζ{\.q}(t)+q(t)=-κ[q(t)- q(t-r)] is unstable when the strength of the feedback (κ) is greater than a critical value (κc). Oscillations of constant amplitude persist when κ=κc. We study the almost-sure asymptotic stability of the oscillator when κ=κc and the system is excited by a two-state Markov noise. For small intensity noise, we construct an asymptotic expansion for the maximal Lyapunov exponent.",

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author = "Nishanth Lingala and {Sri Namachchivaya}, N. and O'Reilly, {Oliver M.} and Volker Wihstutz",

note = "Funding Information: The authors would like to acknowledge the support of the National Science Foundation under Grant no. CMMI 1000906 . Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. Copyright: Copyright 2013 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.probengmech.2012.12.008",

language = "English (US)",

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AU - Lingala, Nishanth

AU - Sri Namachchivaya, N.

AU - O'Reilly, Oliver M.

AU - Wihstutz, Volker

N1 - Funding Information: The authors would like to acknowledge the support of the National Science Foundation under Grant no. CMMI 1000906 . Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. Copyright: Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - An oscillator of the form q̇(t)+2ζq̇(t)+q(t)=-κ[q(t)- q(t-r)] is unstable when the strength of the feedback (κ) is greater than a critical value (κc). Oscillations of constant amplitude persist when κ=κc. We study the almost-sure asymptotic stability of the oscillator when κ=κc and the system is excited by a two-state Markov noise. For small intensity noise, we construct an asymptotic expansion for the maximal Lyapunov exponent.

AB - An oscillator of the form q̇(t)+2ζq̇(t)+q(t)=-κ[q(t)- q(t-r)] is unstable when the strength of the feedback (κ) is greater than a critical value (κc). Oscillations of constant amplitude persist when κ=κc. We study the almost-sure asymptotic stability of the oscillator when κ=κc and the system is excited by a two-state Markov noise. For small intensity noise, we construct an asymptotic expansion for the maximal Lyapunov exponent.

KW - Almost-sure stability

KW - Chatter

KW - Delay differential equation

KW - Lyapunov exponent

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JF - Probabilistic Engineering Mechanics

ER -

Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise

Abstract

Keywords

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