Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation

被引：6

作者：

Feng, Changshui ^{[1
]}

Zhu, Weiqiu ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Mech, State Key Lab Fluid Power Transmiss & Control, Hangzhou 310027, Zhejiang, Peoples R China

来源：

ACTA MECHANICA | 2009年 / 208卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

NONLINEAR OSCILLATORS; SYSTEMS;

D O I：

10.1007/s00707-008-0126-3

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The asymptotic Lyapunov stability with probability one of a Duffing system with time-delayed feedback control under bounded 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 It 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 It 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.

引用

页码：55 / 62

页数：8

共 25 条

[1]

Agrawal AK, 1997, EARTHQ ENG STRUCT D, V26, P1169, DOI 10.1002/(SICI)1096-9845(199711)26:11<1169::AID-EQE702>3.0.CO

[2]

2-S

[3]

[Anonymous], 2003, APPL MECH REV

[4] Stochastic stability of non-gyroscopic viscoelastic systems [J].