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Keywords:
chaos; synchronization; Lur’e system; replacing variables control
chaos; synchronization; Lur’e system; replacing variables control
Summary:
Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur’e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion and frequency- domain criterion, are reviewed and discussed.
References:
[1] Aizerman M. A., Gantmacher F. R.: Absolute Stability of Regulator Systems. Holder-Day Inc. 1964 MR 0183556
[2] Boccaletti S., Kurths J., Osipov G., Valladares D. L., Zhou C. S.: The synchronization of chaotic systems. Phys. Rep. 366 (2002), 1–101 MR 1913567 | Zbl 0995.37022
[3] Curran P. F., Chua L. O.: Absolute stability theory and the synchronization problem. Internat. J. Bifur. Chaos 7 (1997), 1375–1382 MR 1488523 | Zbl 0910.34054
[4] Pecora L. M., Carroll T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821–824 MR 1038263 | Zbl 0938.37019
[5] Pecora L. M., Carroll T. L.: Driving systems with chaotic signals. Phys. Rev. A 44 (1991), 2374–2383
[6] Suykens J. A. K., Curran P. F., Chua L. O.: Robust synthesis for master-slave synchronization of Lur’e systems. IEEE Trans. Circuits and Systems-I 46 (1999), 841–850 Zbl 1055.93549
[7] Suykens J. A. K., Curran P. F., Yang T., Vandewalle, J., Chua L. O.: Nonlinear synchronization of Lur’e systems: dynamic output feedback case. IEEE Trans. Circuits and Systems-I 44 (1997), 1089–1092
[8] Suykens J. A. K., Vandewalle, J., Chua L. O.: Nonlinear synchronization of chaotic Lur’e system. Internat. J. Bifur. Chaos 7 (1997), 1323–1335
[9] Suykens J. A. K., Vandewalle J.: Master-slave synchronization of Lur’e systems. Internat. J. Bifur. Chaos 7 (1997), 665–669 Zbl 0925.93342
[10] Suykens J. A. K., Yalcin M. E., Vandewalle J.: Chaotic systems synchronization. In: Chaos and Bifurcation Control: Theory and Application (G. Chen and X. Yu, eds., Lecture Notes in Control and Information Sciences 292). Springer-Verlag, Hong Kong 2004, pp. 117–135 MR 2014609 | Zbl 1055.34093
[11] Suykens J. A. K., Yang, T., Chua L. O.: Impulsive synchronization of chaotic Lur’s systems by measurement feedback. Internat. J. Bifur. Chaos 8 (1998), 1371–1381
[12] Wang X. F., Wang Z. Q., Chen G. R.: A new criterion for synchronization of coupled chaotic oscillators with application to Chua’s circuits. Internat. J. Bifur. Chaos 9 (1999), 1169–1174
[13] Wu X. F., Wang M. H.: Robust synchronization of chaotic Lur’e systems via replacing variables control. Internat. J. Bifur. Chaos 16 (2006), 3421–3434 MR 2288592 | Zbl 1114.93089
[14] Wu X. F., Zhao Y.: Frequency domain criterion for chaos synchronization of Lur’e systems via state feedback control. Internat. J. Bifur. Chaos 15 (2005), 1145–1154 MR 2152084
[15] Wu X. F., Zhao, Y., Huang X. H.: Some new criteria for lag synchronization of chaotic Lur’e systems by replacing variables control. J. Control Theory Appl. 2 (2004), 259–266 MR 2107247 | Zbl 1134.93035
[16] Wu X. F., Zhao, Y., Zhou S.: Lag synchronization of chaotic Lur’e systems via replacing variables control. Internat. J. Bifur. Chaos 15 (2005), 617–635 MR 2143630 | Zbl 1079.93019
[17] Xie H. M.: Theory and Application of Absolute stability. Science Press, Beijing 1986
[18] Yang T., Chua L. O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits and Systems-I 44 (1997), 976–988 MR 1488197
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