Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation
type: Item
instance of: scholarly article
title: Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation
zbMATH Open document ID: 1202.70116
author: C. S. Feng
author: Weiqiu Zhu
published in: Acta Mechanica
publication date: 2009-10-26T00:00:00Z
review text: First, the authors express the time-delayed feedback control force in terms of system variables without time delay by using generalized harmonic functions. Then, by using the stochastic averaging method, the obtained differential equations are transformed into Itô stochastic differential equations. The asymptotic Lyapunov stability of the system is studied by means of the Lyapunov exponent. The comparison of analytical results with numerical simulations show that the presented procedure yields accurate results when the time delay is less than one averaged period. It is also shown that the time delay in feedback control can destabilize the system.
reviewed by: Yuri N. Sankin
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70L05
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 5620336
zbMATH Keywords: stochastic averaging method
zbMATH Keywords: generalized harmonic functions
zbMATH Keywords: Itô differential equations
MaRDI profile type: Publication
full work available at URL: s00707-008-0126-3
OpenAlex ID: W2048701063
cites work: Q3807934
cites work: Q4427316
cites work: Resonances of a harmonically forced Duffing oscillator with time delay state feedback
cites work: Effects of time delayed position feedback on a van der Pol-Duffing oscillator
cites work: The response of a Duffing-van der Pol oscillator under delayed feedback control
cites work: Stability and dynamics of a controlled van der Pol-Duffing oscillator
cites work: Time delay induced effects on control of nonlinear systems under random excitation
cites work: Stochastic averaging of quasi-integrable Hamiltonian systems with delayed feedback control
cites work: Q4366631
cites work: Stochastic stability of non-gyroscopic viscoelastic systems
cites work: Stochastic averaging of strongly non-linear oscillators under bounded noise excitation
cites work: Responses of strongly non-linear oscillator parametrically excited by random narrow-band noise
cites work: Response statistics of three-degree-of-freedom nonlinear system to narrow-band random excitation
cites work: Q5646734
DOI: 10.1007/S00707-008-0126-3
description: scientific article; zbMATH DE number 5620336