Robust H∞ synchronization of chaotic Lur'e systems

Chaos

Volumn 18, Issue 3, 2008, Pages

  Huang, He ^a   Feng, Gang ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749097505     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2959852     Document Type: Article

References (47)

1. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., and Zhou, C. S., " The synchronization of chaotic systems.," Phys. Rep. 366, 1-101 (2002).
2. Boccaletti, S., Pecora, L. M., and Pelaez, A., " Unifying framework for synchronization of coupled dynamical systems.," Phys. Rev. E 63, 066219 (2001).
3. Boyd, S., EI Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994).
4. Brown, R., and Kocarev, L., " A unifying definition of synchronization for dynamical systems.," Chaos 10, 344-349 (2000).
5. Cao, J., Li, H.-X., and Ho, D. W. C., " Synchronization criteria of Lur'e systems with time-delay feedback control.," Chaos, Solitons Fractals 23, 1285-1298 (2005).
6. Chen, G., and Dong, X., From Chaos to Order-Perspectives, Methodologies, and Applications (World Scientific, Singapore, 1998).
7. Chen, Z., Lin, W., and Zhou, J., " Complete and generalized synchronization in a class of noise perturbed chaotic systems.," Chaos 17, 023106 (2007).
8. Chen, H. F., and Liu, J. M., " Open-loop chaotic synchronization of injection-locked semiconductor lasers with Gigahertz range modulation.," IEEE J. Quantum Electron. 36, 27-34 (2000).
9. Curran, P. F., and Chua, L. O., " Absolute stability theory and the synchronization problem.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1375-1382 (1997).
10. Curran, P. F., Suykens, J. A. K., and Chua, L. O., " Absolute stability theory and master-slave synchronization.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 2891-2896 (1997).
11. Elson, R. C., Selverston, A. I., Huerta, R., Rulkov, N. F., Rabinovich, M. I., and Abarbanel, H. D., " Synchronous behavior of two coupled biological neurons.," Phys. Rev. Lett. 81, 5692 -5695 (1998).
12. Gahinet, P., Nemirovsky, A., Laub, A. J., and Chilali, M., LMI Control Toolbox: For Use With Matlab (The Math Works, Inc., Natick, Massachusetts, 1995).
13. Hale, J. K., and Lunel, S. M. V., Introduction to Functional Differential Equations (Springer-Verlag, New York, 1993).
14. Han, Q.-L., " On designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems.," IEEE Trans. Circuits Syst., I: Regul. Pap. 54, 1573-1583 (2007a).
15. Han, Q.-L., " New delay-dependent synchronization criteria for Lur'e systems using time delay feedback control.," Phys. Lett. A 360, 563-569 (2007b).
16. Hasler, H., " Synchronization principles and applications.," in Circuits and Systems: Tutorials IEEE-ISCAS'94 (IEEE, Piscataway, 1994), pp. 314-326.
17. He, Y., Wen, G., and Wang, Q.-G., " Delay-dependent synchronization criterion for Lur'e systems with delay feedback control.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 3087-3091 (2006).
18. Hramov, A. E., and Koronovskii, A. A., " Generalized synchronization: A modified system approach.," Phys. Rev. E 71, 067201 (2005).
19. Hramov, A. E., and Koronovskii, A. A., " An approach to chaotic synchronization.," Chaos 14, 603-610 (2004).
20. Hramov, A. E., Koronovskii, A. A., and Moskalenko, O. I., " Generalized synchronization onset.," Europhys. Lett. 72, 901-907 (2005a).
21. Hramov, A. E., Koronovskii, A. A., and Moskalenko, O. I., " Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators.," Phys. Lett. A 354, 423-427 (2006).
22. Hramov, A. E., Koronovskii, A. A., and Popov, P. V., " Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising.," Phys. Rev. E 72, 037201 (2005b).
23. Hramov, A. E., Koronovskii, A. A., and Popov, P. V., " Incomplete noise-induced synchronization of spatially extended systems.," Phys. Rev. E 77, 036215 (2008).
24. Huijberts, H., Nijmeijer, H., and Oguchi, T., " Anticipating synchronization of chaotic Lur'e systems.," Chaos 17, 013117 (2007).
25. Kapitaniak, T., and Chua, L. O., " Hyperchaotic attractors of unidirectionally-coupled Chua's circuit.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 477-482 (1994).
26. Kurian, A. J., and Puthusserypady, S., " Chaotic synchronization: A nonlinear predictive filtering approach.," Chaos 16, 013126 (2006).
27. Liao, X., and Chen, G., " Chaos synchronization of general Lur'e systems via time-delay feedback control.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 207-213 (2003).
28. Lin, W., and He, Y., " Complete synchronization of the noise perturbed Chua's circuits.," Chaos 15, 023705 (2005).
29. Madan, R. N., (editor), Chua's Circuit: A Paradigm for Chaos (World Scientific, Singapore, 1993).
30. Pecora, L. M., and Carroll, T. L., " Synchronization in chaotic systems.," Phys. Rev. Lett. 64, 821-824 (1990).
31. Pecora, L. M., Carroll, T. L., Johnson, G. A., and Mar, D. J., " Fundamentals of synchronization in chaotic systems, concepts, and applications.," Chaos 7, 520-543 (1997).
32. Prokhorov, M. D., Ponomarenko, V. I., Gridnev, V. I., Bodrov, M. B., and Bespyatov, A. B., " Synchronization between main rhythmic processes in the human cardiovascular system.," Phys. Rev. E 68, 041913 (2003).
33. Rosenblum, M. G., Pikovsky, A. S., and Kurths, J., " From phase to lag synchronization in coupled chaotic oscillators.," Phys. Rev. Lett. 78, 4193-4196 (1997).
34. Rosenblum, M. G., Pikovsky, A. S., and Kurths, J., " Phase synchronization of chaotic oscillators.," Phys. Rev. Lett. 76, 1804-1807 (1996).
35. Sánchez, E., Matías, M. A., and Ṕrez-Muuzuri, V., " Analysis of synchronization of chaotic systems by noise: An experimental study.," Phys. Rev. E 56, 4068-4071 (1997).
36. Souza, F. O., Palhares, R. M., Mendes, E. M. A., and Tôrres, L. A. B., " Further results on master-slave synchronization of general Lur'e systems with time-varying delay.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, 187-202 (2008).
37. Suykens, J. A. K., Curran, P. F., and Chua, L. O., " Robust synthesis for master-slave synchronization of Lur'e systems.," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 46, 841-850 (1999).
38. Suykens, J. A. K., Curran, P. F., Vandewalle, J., and Chua, L. O., " Robust nonlinear H∞ synchronization of chaotic Lur'e systems.," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 891-904 (1997a).
39. Suykens, J. A. K., Vandewalle, J., and Chua, L. O., " Nonlinear H∞ synchronization of chaotic Lur'e systems.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1323-1335 (1997b).
40. Suykens, J. A. K., Curran, P. F., Yang, T., Vandewalle, J., and Chua, L. O., " Nonlinear H∞ synchronization of Lur'e systems: Dynamic output feedback case.," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 1089-1092 (1997c).
41. Suykens, J. A. K., and Vandewalle, J., " Master-slave synchronization of Lur'e systems.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 665-669 (1997).
42. Toral, R., Mirasso, C. R., Hernández-García, E., and Piro, O., " Analytical and numerical studies of noise-induced synchronization of chaotic systems.," Chaos 11, 665-673 (2001).
43. Vidyasagar, M., Nonlinear Systems Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1993).
44. Wu, C. W., and Chua, L. O., " A unified framework for synchronization and control of dynamical systems.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 979-998 (1994).
45. Xiang, J., Li, Y., and Wei, W., " An improved condition for master-slave synchronization of Lur'e systems with time delay.," Phys. Lett. A 362, 154-158 (2007).
46. Yaļin, M. E., Suykens, J. A. K., and Vandewalle, J., " Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's Circuit.," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 425-429 (2000).
47. Yaļin, M. E., Suykens, J. A. K., and Vandewalle, J., " Master-slave synchronization of Lur'e systems with time-delay.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 1707-1722 (2001).