Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. (English) Zbl 1044.93026

A new method to control and synchronize the chaotic Genesio system is proposed. We can design a nonlinear feedback controller to make the controlled system stable at the origin and two Genesio systems may be synchronized. The stability analysis of the controlled system becomes a simple Hurwitz stability analysis provided that a parameter is chosen suitably. Numerical simulations verified the effectiveness of this method.


93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D15 Stabilization of systems by feedback
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[2] Genesio, R.; Tesi, A., A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems, Automatica, 28, 531-548 (1992) · Zbl 0765.93030
[3] Wu, C. W.; Chua, L. O., A unified framework for synchronization an control of dynamical systems, Int. J. Bifurcat. Chaos, 4, 979-998 (1994) · Zbl 0875.93445
[4] Carroll, T. L.; Pecora, L. M., Synchronizing chaotic circuits, IEEE Trans. Circ. Syst., 38, 453-456 (1993) · Zbl 0800.94100
[5] Tesi, A.; Angeli, A. D.; Genesio, R., On system decomposition for synchronizing chaos, Int. J. Bifurcat. Chaos, 4, 1675-1685 (1994) · Zbl 0875.94003
[6] Liao, T. L., Adaptive synchronization of two Lorenz systems, Chaos, Solitons & Fractals, 9, 1555-1561 (1998) · Zbl 1047.37502
[7] Liu, F.; Ren, Y.; Shan, X. M.; Qiu, Z. L., A linear feedback synchronization theorem for a class of chaotic systems, Chaos, Solitons & Fractals, 13, 723-730 (2002) · Zbl 1032.34045
[8] Richeer, H.; Reinschke, K. J., Local control of chaotic systems-a Lyapunov approach, Int. J. Bifurcat. Chaos, 8, 1565-1973 (1998) · Zbl 0941.93523
[9] Konishi, K.; Hirai, M.; Kokame, H., Sliding mode control for a class of chaotic systems, Phys. Lett. A, 245, 511-517 (1998)
[10] Ott, E.; Grebogi, C.; Yorke, J., Controlling chaos, Phys. Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501
[11] Pyragas, K., Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170, 421-428 (1992)
[12] Chen, G., Chaos on some controllability conditions for chaotic dynamics control, Chaos, Solitons & Fractals, 8, 1461-1470 (1997)
[13] Hwang, C.; Chow, H.; Wang, Y., A new feedback control of a modified chua’s circuit system, Phys. D, 92, 95-100 (1996) · Zbl 0925.93366
[14] Hegazi, A.; Agiza, H. N.; El-Dessoky, M. M., Controlling chaotic behavior for spin generator and Rossler dynamical systems with feedback control, Chaos, Solitons & Fractals, 12, 631-658 (2001) · Zbl 1016.37050
[15] Ramirez, J., Nonlinear feedback for control of chaos from a piecewise linear hysteresis circuit, IEEE Trans. Circ. Syst., 42, 168-172 (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.