Global synchronization of chaotic Lur'e systems via replacing variables control

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results.

[1]  J. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems , 1997 .

[2]  J. Suykens,et al.  Robust synthesis for master-slave synchronization of Lur'e systems , 1999 .

[3]  Guanrong Chen,et al.  Adaptive Synchronization of Chaotic Systems via State or output Feedback Control , 2001, Int. J. Bifurc. Chaos.

[4]  J. Suykens,et al.  Absolute stability theory and master-slave synchronization , 1997 .

[5]  J. Suykens,et al.  Nonlinear H∞ Synchronization of Chaotic Lur'e Systems , 1997 .

[6]  M. Feki.  Observer-based exact synchronization of ideal and mismatched chaotic systems , 2003 .

[7]  Manuel Graña,et al.  Feedback Synchronization of Chaotic Systems , 2003, Int. J. Bifurc. Chaos.

[8]  Xiaofeng Wu,et al.  Some new criteria for lag synchronization of chaotic Lur'e systems by replacing variables control , 2004 .

[9]  Johan A. K. Suykens,et al.  Chaotic systems synchronization , 2003 .

[10]  Guanrong Chen,et al.  Chaos Synchronization of General Lur'e Systems via Time-Delay Feedback Control , 2003, Int. J. Bifurc. Chaos.

[11]  E. M. Shahverdiev,et al.  Parameter mismatches, variable delay times and synchronization in time-delayed systems , 2005 .

[12]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .

[13]  Xiao Fan Wang,et al.  Global Synchronization of a Class of Chaotic Systems with a Scalar Transmitted Signal , 2004, Int. J. Bifurc. Chaos.

[14]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[15]  L. Chua,et al.  Absolute Stability Theory and the Synchronization Problem , 1997 .

[17]  Johan A. K. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems with Time-Delay , 2001, Int. J. Bifurc. Chaos.

[18]  J. Suykens,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback , 1998 .

[19]  J. Suykens,et al.  Nonlinear H/sub /spl infin// synchronization of Lur'e systems: dynamic output feedback case , 1997 .

[20]  J. Suykens,et al.  Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems , 1997 .

[21]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[22]  F. M. Moukam Kakmeni,et al.  A New Synchronization Principle for a Class of Lur'e Systems with Applications in Secure Communication , 2004, Int. J. Bifurc. Chaos.

[23]  Tambe,et al.  Driving systems with chaotic signals. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  Nikolai F. Rulkov,et al.  Experimental observation of synchronized chaos with frequency ratio 1 : 2 , 1996 .

[25]  Guanrong Chen,et al.  A NEW CRITERION FOR SYNCHRONIZATION OF COUPLED CHAOTIC OSCILLATORS WITH APPLICATION TO CHUA'S CIRCUITS , 1999 .

[26]  Jinhu Lu,et al.  Chaos synchronization between linearly coupled chaotic systems , 2002 .

[27]  Leon O. Chua,et al.  ADAPTIVE SYNCHRONIZATION OF CHUA'S OSCILLATORS , 1996 .

[28]  Giuseppe Grassi,et al.  A Novel Framework for Synchronizing via Scalar Signal hyperchaotic Systems with One or Several nonlinearities , 2003, Int. J. Bifurc. Chaos.

[29]  Yeng Chai Soh,et al.  Chaotic cryptosystem with high sensitivity to parameter mismatch , 2003 .

[30]  Jitao Sun,et al.  Delay-dependent stability criteria for coupled chaotic systems via unidirectional linear error feedback approach , 2004 .

[31]  Jinhu Lu,et al.  Synchronization of an uncertain unified chaotic system via adaptive control , 2002 .

[32]  J. Suykens,et al.  Nonlinear H Synchronization of Lur ’ e Systems : Dynamic Output Feedback Case , 1997 .

[33]  Guo-Ping Jiang,et al.  A New Criterion for Chaos Synchronization Using Linear State Feedback Control , 2003, Int. J. Bifurc. Chaos.

[34]  XIAOFENG WU,et al.  Robust Synchronization of Chaotic Lur'e Systems via replacing Variables Control , 2006, Int. J. Bifurc. Chaos.

[35]  Guanrong Chen,et al.  Switching manifold approach to chaos synchronization , 1999 .

[36]  L. O. Chua,et al.  The double scroll family. I: Rigorous of chaos. II: Rigorous analysis of bifurcation phenomena , 1986 .

[37]  J. Suykens,et al.  Master-slave synchronization using dynamic output feedback , 1997 .

[38]  L. Chua,et al.  A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS , 1994 .