A Global Synchronization Theorem for a Class of Chaotic Systems

1998 ◽  
Vol 08 (06) ◽  
pp. 1363-1369 ◽  
Author(s):  
Xiao Fan Wang ◽  
Zhi Quan Wang
Keyword(s):  
Chaotic Systems ◽  
Drive System ◽  
Chaotic Oscillator ◽  
Error Feedback ◽  
Global Synchronization ◽  
Lur’E Systems ◽  
State Variable ◽  
Chaotic Lur’E Systems ◽  
Driving Signal

This Letter proposes a new synchronization theorem for a subclass of chaotic Lur'e systems. We take a specific state variable of the drive system as the driving signal. We prove that globally synchronization can be attained via the simple linear error feedback. The approach is illustrated using Chua's chaotic oscillator and a hyperchaotic oscillator.

GLOBAL SYNCHRONIZATION OF A CLASS OF CHAOTIC SYSTEMS WITH A SCALAR TRANSMITTED SIGNAL

2004 ◽  
Vol 14 (04) ◽  
pp. 1431-1437 ◽  
Author(s):  
JUNGUO LU ◽  
YUGENG XI ◽  
XIAOFAN WANG
Keyword(s):  
Chaotic Systems ◽  
Linear Part ◽  
Feedback Gain ◽  
Chaotic Oscillator ◽  
Hyperchaotic System ◽  
State Variables ◽  
Error Feedback ◽  
Global Synchronization ◽  
Nonlinear Part ◽  
Output Error

This letter proposes a new global synchronization theorem for a class of chaotic systems. Specially, in the synchronization theorem neither the linear part nor the nonlinear part of the chaotic system requires the special structure indicated in [Wang & Wang, 1998]. We take a linear combination of the original system state variables as the scale-driving signal. We prove that the global synchronization can be attained through the simple linear output error feedback. The linear output error feedback gain is a function of a free parameter. We use Chua's chaotic oscillator and Saito's hyperchaotic system to illustrate the applicability of our synchronization scheme and discuss the issues concerning robustness.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

CHAOS SYNCHRONIZATION OF TWO COUPLED DYNAMOS SYSTEMS WITH UNKNOWN SYSTEM PARAMETERS

2004 ◽  
Vol 15 (06) ◽  
pp. 873-883 ◽  
Author(s):  
H. N. AGIZA
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Error Feedback ◽  
Simple Criterion ◽  
Global Synchronization ◽  
System Parameters ◽  
Synchronization Problem ◽  
Unknown System

This paper addresses the synchronization problem of two coupled dynamos systems in the presence of unknown system parameters. Based on Lyapunov stability theory, an active control law is derived and activated to achieve the state synchronization of two identical coupled dynamos systems. By using Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled dynamos systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

2013 ◽  
Vol 275-277 ◽  
pp. 2565-2569
Author(s):  
Lin Xu ◽  
Zhong Liu ◽  
Yun Chen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Numerical Example ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

Nonlinear H∞ Synchronization of Chaotic Lur'e Systems

1997 ◽  
Vol 07 (06) ◽  
pp. 1323-1335 ◽  
Author(s):  
J. A. K. Suykens ◽  
J. Vandewalle ◽  
L. O. Chua
Keyword(s):  
Tracking Error ◽  
Feedback Mechanism ◽  
Channel Noise ◽  
Lur’E Systems ◽  
Synchronization Problem ◽  
Chaotic Lur’E Systems ◽  
Feedback Matrix ◽  
System Theoretical Approach ◽  
Field Modulation ◽  
Synchronization Scheme

In this paper a master-slave synchronization scheme for Lur'e systems is investigated, which consists of vector field modulation by means of the message signal. Using a full state error feedback mechanism and formulating the synchronization problem within the standard plant framework of modern control theory, it is shown how the original message can be recovered for a class of binary-valued continuous time reference inputs or message signals. Input/output properties of the synchronization scheme are analyzed using the system-theoretical approach of dissipativity with a quadratic storage function and a supply rate of finite L2-gain. The feedback matrix is designed such that the influence of the exogenous input on a tracking error is minimized, corresponding to a so-called nonlinear H∞ synchronization scheme. Channel noise is taken into account in the design. The method is illustrated on Chua's circuit and an n-double scroll circuit.

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