Paper Title:
Stochastic Stability of Mathieu-Van Der Pol System with Delayed Feedback Control
  Abstract

The asymptotic Lyapunov stability with probability one of Mathieu-Van der Pol system with time-delayed feedback control under wide-band noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original system, and the asymptotic Lyapunov stability with probability one of the original system can be determined approximately by using the Lyapunov exponent. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. The theoretical results are well verified through digital simulation.

  Info
Periodical
Chapter
Chapter 1: Vibration Engineering
Edited by
Paul P. Lin and Chunliang Zhang
Pages
132-138
DOI
10.4028/www.scientific.net/AMM.105-107.132
Citation
C. S. Feng, S. L. Chen, "Stochastic Stability of Mathieu-Van Der Pol System with Delayed Feedback Control", Applied Mechanics and Materials, Vols. 105-107, pp. 132-138, 2012
Online since
September 2011
Export
Price
$32.00
Share

In order to see related information, you need to Login.

In order to see related information, you need to Login.

Authors: Lin Wu, Jin Cheng Wei, Liu Jie
Chapter 1: Researching and Designing in Mechanical Engineering, Mechatronics, Automation and Control
Abstract:Taking the hyperchaos Rossler system as an example and based on the Lyapunov Stabilization Law, with the parameters unknown, through the...
724
Authors: G. Füsun Alişverişçi
Abstract:With the crank-and-rod exciters, the vibrational conveyers have a trough supported on elastic stands which are rigidly fastened to the trough...
44
Authors: Gui Ling Ju, Wei Hai Sun
Chapter 3: Measurements, Mechatronics, Control and Automation
Abstract:This paper deals with the adaptive control design of stochastic nonholonomic system with uncertainties. The state-input scaling technique,...
692