An H∞ approach to anti-synchronization for chaotic systems

Abstract In this Letter, we propose a new H ∞ anti-synchronization scheme for a general class of chaotic systems. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the H ∞ anti-synchronization controller is presented to not only guarantee stable anti-synchronization but also reduce the effect of external disturbance to an H ∞ norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed anti-synchronization scheme.

[1]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[2]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[3]  Ju H. Park,et al.  H∞ synchronization of chaotic systems via dynamic feedback approach , 2008 .

[4]  Er-Wei Bai,et al.  Sequential synchronization of two Lorenz systems using active control , 2000 .

[5]  Ju H. Park.  Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[6]  Y. Lai,et al.  Observability of lag synchronization of coupled chaotic oscillators. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Oh-Min Kwon,et al.  LMI optimization approach to stabilization of time-delay chaotic systems , 2005 .

[8]  Meng Zhan,et al.  Complete synchronization and generalized synchronization of one-way coupled time-delay systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Zhi-Hong Guan,et al.  Feedback and adaptive control for the synchronization of Chen system via a single variable , 2003 .

[10]  Anton A. Stoorvogel,et al.  The H ∞ control problem: a state space approach , 2000 .

[11]  T. Liao,et al.  H∞ synchronization of chaotic systems using output feedback control design , 2007 .

[12]  Jinde Cao,et al.  Synchronization and anti-synchronization for chaotic systems , 2007 .

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[15]  Zuolei Wang,et al.  Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters , 2009 .

[16]  Jun-an Lu,et al.  Parameter identification and backstepping control of uncertain Lü system , 2003 .

[17]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[18]  Young-Jai Park,et al.  Anti-synchronization of chaotic oscillators , 2003 .

[19]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[20]  Chun-Chieh Wang,et al.  A new adaptive variable structure control for chaotic synchronization and secure communication , 2004 .

[21]  Jinde Cao,et al.  Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification , 2007 .

[22]  Yinping Zhang,et al.  Chaotic synchronization and anti-synchronization based on suitable separation , 2004 .

[23]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[24]  J. A. Laoye,et al.  Synchronization, anti-synchronization and current transports in non-identical chaotic ratchets , 2007 .

[25]  S. S. Yang,et al.  Generalized Synchronization in Chaotic Systems , 1998 .

[26]  Chuandong Li,et al.  Anti-Synchronization of a Class of Coupled Chaotic Systems via Linear Feedback Control , 2006, Int. J. Bifurc. Chaos.

[27]  Jianbo Liu,et al.  Anti-phase synchronization in coupled map lattices , 2000 .

[28]  Guanrong Chen,et al.  Some observer-based criteria for discrete-time generalized chaos synchronization , 2002 .