Stochastic stability of quasi-integrable Hamiltonian systems with time delay by using Lyapunov function method

被引：5

作者：

Ling Quan ^{[1
]}

Jin XiaoLing ^{[1
]}

Huang ZhiLong ^{[2
]}

机构：

[1] Zhejiang Univ, Dept Mech, Hangzhou 310027, Peoples R China

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

来源：

SCIENCE CHINA-TECHNOLOGICAL SCIENCES | 2010年 / 53卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Lyapunov stability; Lyapunov function; time delay; stochastic averaging; ASYMPTOTIC STABILITY; LINEAR-SYSTEMS; STABILIZATION;

D O I：

10.1007/s11431-010-0071-y

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging method. First, a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay. Then, stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system, and after that the Lyapunov function of the averaged It equation is taken as the optimal linear combination of the corresponding independent first integrals in involution. Finally, the stability of the system is determined by using the largest eigenvalue of the linearized system. Two examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.

引用

页码：703 / 712

页数：10

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