Synchronization Criterion for Lur’e Systems via Delayed PD Controller

In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur’e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

[1]  L. Chua,et al.  HYPERCHAOTIC ATTRACTORS OF UNIDIRECTIONALLY-COUPLED CHUA’S CIRCUITS , 1994 .

[2]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[3]  George Leitmann,et al.  Dynamics and Control , 2020, Fundamentals of Robotics.

[4]  Q. Han.  New delay-dependent synchronization criteria for Lur'e systems using time delay feedback control , 2007 .

[5]  Shouming Zhong,et al.  Design of PD controller for master-slave synchronization of Lur'e systems with time-delay , 2009, Appl. Math. Comput..

[6]  Guanrong Chen,et al.  Chaos Synchronization of General Lur'e Systems via Time-Delay Feedback Control , 2003, Int. J. Bifurc. Chaos.

[7]  Jinde Cao,et al.  Master-Slave Synchronization of Lur'e Systems Based on Time-Varying Delay Feedback Control , 2007, Int. J. Bifurc. Chaos.

[8]  Qing-Guo Wang,et al.  Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays , 2006 .

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

[10]  Mohammad Hosseini,et al.  Robust control of uncertain systems with time varying delays in control input , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[11]  J. H. Park,et al.  Asymptotic Stability of Neutral Systems with Multiple Delays , 1999 .

[12]  Han-Xiong Li,et al.  Master-Slave Synchronization of General Lur'e Systems with Time-Varying Delay and Parameter Uncertainty , 2006, Int. J. Bifurc. Chaos.

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

[14]  Jianjiang Yu,et al.  Delay-range-dependent synchronization criterion for Lur’e systems with delay feedback control , 2009 .

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

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

[17]  Firdaus E. Udwadia,et al.  Time-Delayed Positive Velocity Feedback Control Design for Active Control of Structures , 2006 .

[18]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[19]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[20]  Wei Xing Zheng,et al.  Global chaos synchronization with channel time-delay , 2004 .

[21]  Oh-Min Kwon,et al.  Delay-independent absolute stability for time-delay Lur'e systems with sector and slope restricted nonlinearities , 2008 .

[22]  Fernando de Oliveira Souza,et al.  Further Results on Master-Slave Synchronization of General Lur'e Systems with Time-Varying Delay , 2008, Int. J. Bifurc. Chaos.

[23]  Qing-Long Han,et al.  On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[25]  H.F. Chen,et al.  Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation , 2000, IEEE Journal of Quantum Electronics.

[26]  Ju H. Park,et al.  A note on stability of neutral delay-differential systems , 1999 .