Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays

The aim of this paper is to propose an output coupling and feedback scheme, which is not only to guarantee the asymptotic synchronization between the master and the slave chaotic systems with multiple time-delays but also to attenuate the effects of noise perturbation on the overall error system to a prescribed level in terms of the performance index H∞-norm. The output coupling and feedback gain is derived on the basis of the Lyapunov theory and the linear matrix inequality (LMI) technique. Some numerical examples are given to demonstrate the effectiveness of the main results.

[1]  Jinde Cao,et al.  Synchronization criteria of Lur’e systems with time-delay feedback control , 2005 .

[2]  Peter Liu,et al.  LMI-based fuzzy chaotic synchronization and communications , 2001, IEEE Trans. Fuzzy Syst..

[3]  Wen Yu.  Passive equivalence of chaos in Lorenz system , 1999 .

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

[5]  Jitao Sun,et al.  Global synchronization criteria with channel time-delay for chaotic time-delay system , 2004 .

[6]  S. Tong,et al.  Guaranteed cost control of time-delay chaotic systems via memoryless state feedback , 2007 .

[7]  Yi Zhao,et al.  Frequency Domain Criterion for Chaos Synchronization of Lur'e Systems via Linear State Error Feedback Control , 2005, Int. J. Bifurc. Chaos.

[8]  Peter Liu,et al.  Secure communications of chaotic systems with robust performance via fuzzy observer-based design , 2001, IEEE Trans. Fuzzy Syst..

[9]  J. Yan,et al.  H 8 controlling hyperchaos of the Rssler system with input nonlinearity , 2004 .

[10]  Her-Terng Yau,et al.  Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems , 2006 .

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

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

[13]  Juhn-Horng Chen,et al.  Controlling chaos and chaotification in the Chen–Lee system by multiple time delays , 2008 .

[14]  Juan Gonzalo Barajas-Ramírez,et al.  Fuzzy Chaos Synchronization via sampled Driving Signals , 2004, Int. J. Bifurc. Chaos.

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

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

[17]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[18]  Chang-Hua Lien,et al.  Robust H∞ control for uncertain T–S fuzzy systems with state and input delays , 2008 .

[19]  P. Saha,et al.  Multiple delay Rössler system—Bifurcation and chaos control , 2008 .

[20]  Ju H. Park,et al.  Guaranteed cost control of time-delay chaotic systems , 2006 .

[21]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[22]  Peter Liu,et al.  Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[23]  T. Liao.  Observer-based approach for controlling chaotic systems , 1998 .

[24]  C. Lien.  H∞ non-fragile observer-based controls of dynamical systems via LMI optimization approach , 2007 .

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

[26]  Aizhong Lei,et al.  Impulse tuning of Chua chaos , 2005 .

[27]  Wang Fu-zhong,et al.  LMI approach to reliable H ∞ control of linear systems , 2006 .

[28]  José Manoel Balthazar,et al.  On an optimal control design for Rössler system , 2004 .