Hinfinity synchronization of time-delayed chaotic systems

Abstract This paper considers H ∞ synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an H ∞ norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

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

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

[3]  Vicente Pérez-Muñuzuri,et al.  Autowaves for Image Processing on a Two-Dimensional CNN Array of Excitable Nonlinear Circuits: Flat and Wrinkled Labyrinths V. Perez-Mufiuzuri, V. Perez-Villar, and Leon 0. Chua, Fellow, ZEEE , 1993 .

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

[5]  Furong Gao,et al.  Adaptive control of chaotic continuous-time systems with delay , 1998 .

[6]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[7]  A. Stoorvogel.  The H∞ control problem , 1992 .

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

[9]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[10]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[11]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

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

[13]  Wei Zhu,et al.  Global impulsive exponential synchronization of time-delayed coupled chaotic systems , 2008 .

[14]  Ju H. Park.  Stability criterion for synchronization of linearly coupled unified chaotic systems , 2005 .

[15]  Ju H. Park.  Chaos synchronization of a chaotic system via nonlinear control , 2005 .

[16]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

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

[18]  P. Das,et al.  Chaos in an effective four-neuron neural network , 1991 .

[19]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

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

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

[22]  S. M. Lee,et al.  Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control , 2007 .

[23]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[24]  James Lam,et al.  LMI synthesis of H2 and mixed H2/H∞ controllers for singular systems , 2003, IEEE Trans. Circuits Syst. II Express Briefs.