Synchronization of chaotic systems under sampled-data control

The problem of global asymptotical synchronization of chaotic Lur’e systems using sampled-data controller is considered in this paper. Sufficient conditions are obtained in terms of effective synchronization linear matrix inequality using a piecewise sawtooth structure of the sampling in time by constructing the new discontinuous Lyapunov functionals. The sampled-data feedback control gain is obtained from the derived condition. The Chua system and horizontal platform system are taken for numerical demonstration to show the effectiveness of the proposed condition.

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

[2]  Louis M. Pecora,et al.  Synchronizing chaotic systems , 1993, Optics & Photonics.

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

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

[5]  Tao Yang Control of Chaos Using Sampled-Data Feedback Control , 1998 .

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

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

[8]  M. Boutayeb,et al.  Generalized state-space observers for chaotic synchronization and secure communication , 2002 .

[9]  Wei Xing Zheng,et al.  Integral-observer-based chaos synchronization , 2006, IEEE Trans. Circuits Syst. II Express Briefs.

[10]  Qing-Guo Wang,et al.  Delay-Dependent Synchronization Criterion for Lur'e Systems with Delay Feedback Control , 2006, Int. J. Bifurc. Chaos.

[11]  David J. Hill,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  Jeremy S. Smith,et al.  Morphological Lifting Scheme for Current Transformer Saturation Detection and Compensation , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Fernando de Oliveira Souza,et al.  Robust Hinfinity Control for Master-Slave Synchronization of Lur'e Systems with Time-Delay Feedback Control , 2008, Int. J. Bifurc. Chaos.

[14]  David J. Hill,et al.  Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  H. Lam,et al.  Sampled-data fuzzy controller for continuous nonlinear systems , 2008 .

[16]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  S. M. Lee,et al.  Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control , 2009 .

[18]  Liyong Niu,et al.  A revisit to synchronization of Lurie systems with time-delay feedback control , 2009 .

[19]  Min Wu,et al.  Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Ying Yang,et al.  Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks , 2010 .

[21]  Kun Liu,et al.  Stability of linear systems with general sawtooth delay , 2010, IMA J. Math. Control. Inf..

[22]  D. H. Ji,et al.  Synchronization of neutral complex dynamical networks with coupling time-varying delays , 2011 .

[23]  S. M. Lee,et al.  Secure communication based on chaotic synchronization via interval time-varying delay feedback control , 2011 .

[24]  Q. Han,et al.  Master–slave synchronization criteria for horizontal platform systems using time delay feedback control , 2011 .

[25]  S. Jeeva Sathya Theesar,et al.  Synchronization of chaotic nonlinear continuous neural networks with time-varying delay , 2011, Cognitive Neurodynamics.

[26]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[27]  S. Jeeva Sathya Theesar,et al.  Delay-Dependent Exponential Synchronization Criteria for Chaotic Neural Networks with Time-Varying Delays , 2012 .

[28]  Lamberto Rondoni,et al.  Multi-image encryption based on synchronization of chaotic lasers and iris authentication , 2012 .