Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

2010 ◽  
Vol 19 (3) ◽  
pp. 030505 ◽  
Author(s):  
Zhang Hong-Bin ◽  
Xia Jian-Wei ◽  
Yu Yong-Bin ◽  
Dang Chuang-Yin
Keyword(s):  
Feedback Control ◽  
Lyapunov Functions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Quadratic Lyapunov Functions

Controlling chaotic Chua's circuit based on piecewise quadratic Lyapunov functions method

2004 ◽  
Vol 22 (5) ◽  
pp. 1053-1061 ◽  
Author(s):  
Hongbin Zhang ◽  
Chunguang Li ◽  
Jian Zhang ◽  
Xiaofeng Liao ◽  
Juebang Yu
Keyword(s):  
Lyapunov Functions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Quadratic Lyapunov Functions ◽  
Lyapunov Functions Method

A new feedback control of a modified Chua's circuit system

1996 ◽  
Vol 92 (1-2) ◽  
pp. 95-100 ◽  
Author(s):  
Chi-Chuan Hwang ◽  
Hao-Yun Chow ◽  
Yung-Kun Wang
Keyword(s):  
Feedback Control ◽  
Chua’S Circuit ◽  
Chua's Circuit

scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

scholarly journals A linear continuous feedback control of Chua's circuit

1997 ◽  
Vol 8 (9) ◽  
pp. 1507-1515 ◽  
Author(s):  
Chi-Chuan Hwang ◽  
Hsieh Jin-Yuan ◽  
Lin Rong-Syh
Keyword(s):  
Feedback Control ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Continuous Feedback

CONTROLLING CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 139-149 ◽  
Author(s):  
GUANRONG CHEN ◽  
XIAONING DONG
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Control Process ◽  
Periodic Signal ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Simulation Results ◽  
Feedback Control Strategy

The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the well-known Chua's circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. Simple sufficient conditions for the controllability of this particular circuit are established. Simulation results are included to visualize the control process. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate periodic-signal generator to the original circuit.

ANALYSIS ON THE GLOBALLY EXPONENT SYNCHRONIZATION OF CHUA'S CIRCUIT USING ABSOLUTE STABILITY THEORY

2005 ◽  
Vol 15 (12) ◽  
pp. 3867-3881 ◽  
Author(s):  
XIAOXIN LIAO ◽  
PEI YU
Keyword(s):  
Control Systems ◽  
Stability Theory ◽  
Lyapunov Functions ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
Absolute Stability Theory

In this paper, the absolute stability theory and methodology for nonlinear control systems are employed to study the well-known Chua's circuit. New results are obtained for the globally exponent synchronization of two Chua's circuits. The explicit formulas can be easily applied in practice. With the aid of constructing Lyapunov functions, sufficient conditions are derived, under which two (drive-response) Chua's circuits are globally and exponentially synchronized, even if the motions of the systems are divergent to infinity. Numerical simulation results are given to illustrate the theoretical predictions.

GLOBAL ANALYSIS ON n-SCROLL CHAOTIC ATTRACTORS OF MODIFIED CHUA'S CIRCUIT

2009 ◽  
Vol 19 (01) ◽  
pp. 135-157 ◽  
Author(s):  
FEI XU ◽  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Feedback Control ◽  
Global Analysis ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Nonlinear Feedback ◽  
Control Laws ◽  
Chua's Circuit ◽  
Constructive Feedback ◽  
Globally Attractive

In this paper, we present a further mathematical study on the report of existence of n-scroll chaotic attractors in a modified Chua's circuit. A series of results based on mathematical theory are given. First, we show that the chaotic attractors of the modified Chua's circuit are globally attractive, with estimations given for the globally attractive set and positive invariant set. Then, we study the positions, number and local stability of the equilibrium points. We also design simple feedback control laws to globally exponentially stabilize any given equilibrium point. Finally, we use the theory and methodology of absolute stability of Luré nonlinear control systems and nonlinear feedback control to exponentially synchronize two modified Chua's circuits with the same structure. The design of constructive feedback control laws for synchronization is also discussed.

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