Abstract
In this paper, the concept of practical stabilization for nonlinear systems is introduced and the practical stabilization of uncertain Duffing-Holmes control systems with unknown actuator nonlinearity is explored. Based on the time-domain approach with differential inequalities, a single control is presented such that the practical stabilization for a class of uncertain Duffing-Holmes systems with unknown actuator nonlinearity can be achieved. Moreover, both of the guaranteed exponential convergence rate and convergence radius can be correctly calculated Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results.

Keywords
Practical synchronization, Chaotic system, uncertain Duffing-Holmes systems, unknown actuator nonlinearity, Chaos suppression

Cite this paper
Yeong-Jeu Sun, Chaos suppression and practical stabilization of uncertain Duffing-Holmes control systems with unknown actuator nonlinearity , SCIREA Journal of Electrical Engineering. Volume 3, Issue 1, February 2018 | PP. 1-12.

References

[ 1 ]	X. Liu, L. Bo, Y. Liu, Y. Zhao, Y. Zhao, J. Zhang, N. Hu, S. Fu, M. Deng, “Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system,” Journal of Sound and Vibration, vol. 405, pp. 175-186, 2017.
[ 2 ]	V. Wiggers, P. C. Rech, “Multistability and organization of periodicity in a Van der Pol-Duffing oscillator,” Chaos, Solitons & Fractals, vol. 103, pp. 632-637, 2017.
[ 3 ]	H. Shi, W. Li, “Research on weak resonance signal detection method based on Duffing oscillator,” Procedia Computer Science, vol. 107, pp. 460-465, 2017.
[ 4 ]	J. Niu, Y. Shen, S. Yang, S. Li, “Analysis of Duffing oscillator with time-delayed fractional-order PID controller,” International Journal of Non-Linear Mechanics, vol. 92, pp. 66-75, 2017.
[ 5 ]	J. Kengne, Z. N. Tabekoueng, H. B. Fotsin, “Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators,” Communications in Nonlinear Science and Numerical Simulation, vol. 36, pp. 29-44, 2016.
[ 6 ]	J. Li, M. Mao, Y. Zhang, “Simpler ZD-achieving controller for chaotic systems synchronization with parameter perturbation, model uncertainty and external disturbance as compared with other controllers,” Optik-International Journal for Light and Electron Optics, vol. 131, pp. 364-373, 2017.
[ 7 ]	H. Tirandaz, A. K. Mollaee, “Modified function projective feedback control for time-delay chaotic Liu system synchronization and its application to secure image transmission,” Optik-International Journal for Light and Electron Optics, vol. 147, pp. 187-196, 2017.
[ 8 ]	H. P. Ren, C. Bai, Q. Kong, M. S. Baptista, C. Grebogi, “A chaotic spread spectrum system for underwater acoustic communication,” Physica A: Statistical Mechanics and its Applications, vol. 478, pp. 77-92, 2017.
[ 9 ]	K. B. Deng, R. X. Wang, C. L. Li, Y. Q. Fan, “Tracking control for a ten-ring chaotic system with an exponential nonlinear term,” Optik - International Journal for Light and Electron Optics, vol. 130, pp. 576-583, 2017.
[ 10 ]	E. M. Bollt, “Regularized forecasting of chaotic dynamical systems,” Chaos, Solitons & Fractals, vol. 94, pp. 8-15, 2017.
[ 11 ]	M. J. Mahmoodabadi, R. A. Maafi, M. Taherkhorsandi, “An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems,” Applied Soft Computing, vol. 52, pp. 1191-1199, 2017.
[ 12 ]	W. Jiang, H. Wang, J. Lu, G. Cai, W. Qin, “Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control,” Journal of the Franklin Institute, vol. 354, pp. 4838-4860, 2017.
[ 13 ]	G. Xu, J. Xu, C. Xiu, F. Liu, Y. Zang, “Secure communication based on the synchronous control of hysteretic chaotic neuron,” Neurocomputing, vol. 227, pp. 108-112, 2017.