Stochastic Stability of Mathieu-Van der Pol System with Delayed Feedback Control
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 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 iIt (o) 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.
Stochastic stability Lyapunov exponent Delayed feedback control Stochastic averaging
Changshui Feng Shuanglin Chen
Institute of Mechatronic Engineering, Hangzhou Dianzi University Hangzhou 310018, Peoples Republic of China
国际会议
上海
英文
132-138
2011-10-21（万方平台首次上网日期，不代表论文的发表时间）