scholarly journals DEFINING THE CONTROLLING CONDITIONS OF LOW-DIMENSIONAL CHAOTIC SYSTEMS CONTROLLED BY TIME DELAYED FEEDBACK

2001 ◽  
Vol 50 (10) ◽  
pp. 1871
Author(s):  
CHEN YAN-YAN ◽  
PENG JIAN-HUA ◽  
SHEN QI-HONG ◽  
WEI JUN-JIE
Keyword(s):  
Chaotic Systems ◽  
Delayed Feedback ◽  
Low Dimensional ◽  
Time Delayed Feedback

Consistency properties of chaotic systems driven by time-delayed feedback

2018 ◽  
Vol 97 (4) ◽  
Author(s):  
T. Jüngling ◽  
M. C. Soriano ◽  
N. Oliver ◽  
X. Porte ◽  
I. Fischer
Keyword(s):  
Chaotic Systems ◽  
Delayed Feedback ◽  
Consistency Properties ◽  
Time Delayed Feedback

MASTER-SLAVE SYNCHRONIZATION OF NONAUTONOMOUS CHAOTIC SYSTEMS AND ITS APPLICATION TO ROTATING PENDULUMS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250147 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Phase Locked Loops ◽  
Linear Matrix ◽  
Delayed Feedback Controller ◽  
Delay Dependent ◽  
Time Delayed Feedback

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS

2003 ◽  
Vol 13 (01) ◽  
pp. 193-205 ◽  
Author(s):  
XINPING GUAN ◽  
CAILIAN CHEN ◽  
HAIPENG PENG ◽  
ZHENGPING FAN
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Error Control ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Time Delayed Feedback

This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

DELAYED FEEDBACK CONTROL OF CHAOTIC SYSTEMS WITH DRY FRICTION

2002 ◽  
Vol 12 (08) ◽  
pp. 1877-1883 ◽  
Author(s):  
UGO GALVANETTO
Keyword(s):  
Dry Friction ◽  
Chaotic Systems ◽  
Control Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Chaotic Attractors ◽  
Unstable Periodic Orbits ◽  
Numerical Techniques ◽  
The Stability ◽  
Time Delayed Feedback

This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the stability of the orbit but does not affect the orbit itself.

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