Asymptotic Lyapunov stability with probability one of quasi-integrable Hamiltonian systems with delayed feedback control

Automatica ◽  
2008 ◽  
Vol 44 (7) ◽  
pp. 1923-1928 ◽  
Author(s):  
Z.H. Liu ◽  
W.Q. Zhu
Keyword(s):  
Feedback Control ◽  
Hamiltonian Systems ◽  
Lyapunov Stability ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Integrable Hamiltonian Systems

Stochastic Stability of Mathieu-Van Der Pol System with Delayed Feedback Control

2011 ◽  
Vol 105-107 ◽  
pp. 132-138
Author(s):  
Chang Shui Feng ◽  
Shuang Lin Chen
Keyword(s):  
Time Delay ◽  
Lyapunov Exponent ◽  
Feedback Control ◽  
Lyapunov Stability ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Time Delayed Feedback

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.

Giant Improvement of Time-Delayed Feedback Control by Spatio-Temporal Filtering

2002 ◽  
Vol 89 (7) ◽  
Author(s):  
Nilüfer Baba ◽  
Andreas Amann ◽  
Eckehard Schöll ◽  
Wolfram Just
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Temporal Filtering ◽  
Spatio Temporal ◽  
Time Delayed Feedback
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