A passivity based synchronization between two different chaotic systems

In this paper, we propose a new passivity-based synchronization method for two different chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the passivity-based controller is presented to make the synchronization error system between two different chaotic systems not only passive but also asymptotically stable. It is shown that the proposed controller can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. As an application of the proposed method, the synchronization problem between Rossler system and Genesio-Tesi system is investigated.

[1]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

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

[3]  Heng-Hui Chen,et al.  Chaos synchronization between two different chaotic systems via nonlinear feedback control , 2009 .

[4]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[5]  Faqiang Wang,et al.  Synchronization of unified chaotic system based on passive control , 2007 .

[6]  Karim Kemih,et al.  Control of nuclear spin generator system based on passive control , 2009 .

[7]  V. Lakshmikantham,et al.  Nonlinear Analysis: Theory, Methods and Applications , 1978 .

[8]  C. Ahn.  Fuzzy delayed output feedback synchronization for time-delayed chaotic systems , 2010 .

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

[10]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[11]  M. T. Yassen,et al.  Chaos synchronization between two different chaotic systems using active control , 2005 .

[12]  Choon Ki Ahn,et al.  An H∞ approach to anti-synchronization for chaotic systems , 2009 .

[13]  Ruihong Li,et al.  Synchronization of two different chaotic systems with unknown parameters , 2007 .

[14]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

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

[16]  Choon Ki Ahn,et al.  Output feedback ℋ∞ synchronization for delayed chaotic neural networks , 2009 .

[17]  C. Ahn.  T–S fuzzy ℋ∞ synchronization for chaotic systems via delayed output feedback control , 2010 .

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

[19]  H. Salarieh,et al.  Adaptive synchronization of two different chaotic systems with time varying unknown parameters , 2008 .

[20]  王发强,et al.  Synchronization of hyperchaotic Lorenz system based on passive control , 2006 .

[21]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[22]  O. Rössler.  An equation for continuous chaos , 1976 .

[23]  Ju H. Park.  A note on synchronization between two different chaotic systems , 2009 .

[24]  T. Chai,et al.  Adaptive synchronization between two different chaotic systems with unknown parameters , 2006 .

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

[26]  Lu Jun-An,et al.  Passive control and synchronization of hyperchaotic Chen system , 2008 .

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

[28]  R. Massey.  From chaos to order? , 1986, Connecticut medicine.

[29]  Yongguang Yu.  Adaptive synchronization of a unified chaotic system , 2008 .

[30]  Du Qu Wei,et al.  Passivity-based adaptive control of chaotic oscillations in power system , 2007 .

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

[32]  Lee Sun-Jin.  From Chaos to Order , 2011 .

[33]  M. T. Yassen,et al.  Adaptive synchronization of two different uncertain chaotic systems [rapid communication] , 2005 .

[34]  Malek Benslama,et al.  PASSIVITY-BASED CONTROL OF CHAOTIC L ¨ US YSTEM , 2006 .

[35]  Guo-Hui Li,et al.  Generalized projective synchronization between two different chaotic systems using active backstepping control , 2006 .