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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Bibliographic Details
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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Summary: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.
ISSN:0266-8920
1878-4275
DOI:10.1016/j.probengmech.2012.12.008