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

An oscillator of the form q¨(t)+2ζq˙(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 exci...

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Published in:Probabilistic engineering mechanics 2013-04, Vol.32, p.21-30
Main Authors: Lingala, Nishanth, Sri Namachchivaya, N., O'Reilly, Oliver M., Wihstutz, Volker
Format: Article
Language:English
Subjects:
Almost-sure stability
Asymptotic properties
Chatter
Delay differential equation
Excitation
Feedback
Lyapunov exponent
Markov processes
Noise
Oscillations
Oscillators
Stability
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description An oscillator of the form q¨(t)+2ζq˙(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. ► First non-zero term in the asymptotic expansion of the maximal Lyapunov exponent. ► Oscillator with delay feedback can be stabilized by multiplicative noise. ► Chatter suppression in machining using random perturbations of structural parameters.
doi_str_mv 10.1016/j.probengmech.2012.12.008
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subjects Almost-sure stability
Asymptotic properties
Chatter
Delay differential equation
Excitation
Feedback
Lyapunov exponent
Markov processes
Noise
Oscillations
Oscillators
Stability
title Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise
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