Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays

Synchronization under output feedback control with multiple random time delays is studied, using the paradigm in nonlinear physics—Chua’s circuit. Compared with other synchronization control methods, output feedback control with multiple random delay is superior for a realistic synchronization application to secure communications. Sufficient condition for global stability of delay-dependent synchronization is established based on the LMI technique. Numerical simulations fully support the analytical approach, in spite of the random delays.

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

[2]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[3]  Joshua E. S. Socolar,et al.  Controlling extended systems with spatially filtered, time-delayed feedback , 1996, chao-dyn/9612013.

[4]  Daolin Xu,et al.  Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems , 2005 .

[5]  Changchun Hua,et al.  Synchronization of chaotic systems based on PI observer design , 2005 .

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

[7]  N. Buric,et al.  Synchronization of hyperchaotic systems with delayed bidirectional coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

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

[10]  Daniel J. Gauthier,et al.  Comment on ``Dynamic Control of Cardiac Alternans'' , 1997 .

[11]  Xiao-Song Yang,et al.  Concepts of synchronization in dynamical systems , 1999 .

[12]  William L. Luyben,et al.  Process Modeling, Simulation and Control for Chemical Engineers , 1973 .

[13]  E. M. Shahverdiev,et al.  Synchronization in systems with multiple time delays. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Guilin Wen,et al.  Observer-based control for full-state projective synchronization of a general class of chaotic maps in any dimension , 2004 .

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

[16]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[17]  Jin-Hua She,et al.  New delay-dependent stability criteria and stabilizing method for neutral systems , 2004, IEEE Trans. Autom. Control..

[18]  Morgül,et al.  Observer based synchronization of chaotic systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Min Wu,et al.  Robust stability for delay Lur'e control systems with multiple nonlinearities , 2005 .

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

[21]  C Masoller,et al.  Random delays and the synchronization of chaotic maps. , 2005, Physical review letters.

[22]  L. Glass,et al.  DYNAMIC CONTROL OF CARDIAC ALTERNANS , 1997 .

[23]  M. T. Yassen,et al.  Adaptive synchronization of Rossler and Lü systems with fully uncertain parameters , 2005 .

[24]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[25]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[26]  Ulrich Parlitz,et al.  Stabilizing unstable steady states using multiple delay feedback control. , 2004, Physical review letters.

[27]  Daniel J. Gauthier,et al.  Analysis and comparison of multiple-delay schemes for controlling unstable fixed points of discrete maps , 1998 .

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