Stochastic stability of Duffing-Mathieu system with delayed feedback control under white noise excitation

被引：8

作者：

Feng, C. S. ^{[1
]}

Chen, S. L. ^{[1
]}

机构：

[1] Hangzhou Dianzi Univ, Inst Mechatron Engn, Hangzhou 310018, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2012年 / 17卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Stochastic stability; Lyapunov exponent; Delayed feedback control; Stochastic averaging; INTEGRABLE HAMILTONIAN-SYSTEMS; TIME-DELAY; NONLINEAR OSCILLATORS; ACTIVE CONTROL;

D O I：

10.1016/j.cnsns.2012.01.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The asymptotic Lyapunov stability with probability one of Duffing-Mathieu system with time-delayed feedback control under white-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 Ito 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 Ito equations is derived. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. Meanwhile, the stability conditions for the system with different time delays are also obtained. The theoretical results are well verified through digital simulation. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：3763 / 3771

页数：9

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