“H-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input”

Authors: Bo Wang, Peng Shi, Hamid Reza Karimi and Jun Wang,
Affiliation: Xihua University, University of Glamorgan, University of Agder and Victoria University
Reference: 2012, Vol 33, No 1, pp. 27-34.

Keywords: Chaos; Synchronization; Robust control; Disturbance

Abstract: This paper is concerned with the robust control problems for the synchronization of master-slave chaotic systems with disturbance input. By constructing a series of Lyapunov functions, novel H-Infinity robust synchronization controllers are designed, whose control regulation possess the characteristic of simpleness and explicitness. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed techniques.

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DOI forward links to this article:
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[23] Naeimadeen Noghredani and Naser Pariz (2021), doi:10.1007/s42452-021-04244-w
[24] Fazhi Song, Yang Liu, Dong Shen, Li Li and Jiubin Tan (2022), doi:10.1109/TIE.2022.3142428
[25] Fazhi Song, Yang Liu, Yue Dong, Xinkai Chen and Jiubin Tan (2024), doi:10.1109/TIM.2024.3413202
References:
[1] Ahn, C. Song, K. (2011). H2-Hinf filtering for time-delayed switched hopfield neural networks, International Journal of Innovative Computing, Information and Control. 7:1831--1844.
[2] Basin, M., Shi, P., Calderon-Alvarez, D. (2011). Central suboptimal H-Inf control design for nonlinear polynomial systems, Int. J. of System Sciences, 42:801--808 doi:10.1080/00207721.2010.543491
[3] Chen, H. (2009). Chaos control and global synchronization of liu chaotic systems using linear balanced feedback control, Chaos, Solitons and Fractals, 40:466--473 doi:10.1016/j.chaos.2007.07.098
[4] Effa, J., Essimbi, B., Mucho-Ngundam, J. (2009). Synchronization of colpitts oscillators with different orders, Communications in Nonlinear Science and Numerical Simulation, 14:1590--1597 doi:10.1016/j.cnsns.2008.03.019
[5] Fujisaka, H. Yamada, T. (1983). Stability theory of synchronized motion in coupled-oscillator systems, Progress of theoretical physics, 69:32--47 doi:10.1143/PTP.69.32
[6] He, Z., Wu, L., Su, X. (2009). H-Inf control of linear positive systems: Continuous- and discrete-time cases, Intl. Journal of Innovative Computing, Information and Control, 5:1747--1756.
[7] Huang, C., Cheng, K., Yan, J. (2009). Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties, Communications in Nonlinear Science and Numerical Simulation, 14:2784--2792 doi:10.1016/j.cnsns.2008.09.017
[8] Karimi, H.R. (2011). Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations, Int. J. Control, Automation, and Systems, 9:671--680 doi:10.1007/s12555-011-0408-8
[9] Karimi, H.R. (2012). A sliding mode approach to H-Inf synchronization of master-slave time-delays systems with markovian jumping parameters and nonlinear uncertainties, J. of the Franklin Institute, 349:1480--1496 doi:10.1016/j.jfranklin.2011.09.015
[10] Karimi, H.R. Gao, H. (2010). New delay-dependent exponential H-Inf synchronization for uncertain neural networks with mixed time-delays, IEEE Trans. on Systems, Man and Cybernetics, Part B, 40:173--185 doi:10.1109/TSMCB.2009.2024408
[11] Karimi, H.R., Zapateiro, M., Luo, N. (2012). Adaptive synchronization of master-slave systems with mixed neutral and discrete time-delays and nonlinear perturbations, Asian Journal of Control, 14:251--257 doi:10.1002/asjc.439
[12] Kuntanapreeda, S. (2009). Chaos synchronization of unified chaotic systems via lmi, Physics Letters A, 373:2837--2840 doi:10.1016/j.physleta.2009.06.006
[13] Liu, M., Shi, P., Zhang, L., Zhao, X. (2011). Fault-tolerant control for nonlinear markovian jump systems via proportional and derivative sliding mode observer, IEEE Trans on Circuits and Systems I: Regular Papers, 58:2755--2764 doi:10.1109/TCSI.2011.2157734
[14] Luo, C. (2009). Theory for synchronization of dynamical systems, Communications in Nonlinear Science and Numerical Simulation, 14:1901--1951 doi:10.1016/j.cnsns.2008.07.002
[15] Pecora, L. Carroll, T. (1990). Synchronization in chaotic systems, Communications in Nonlinear Science and Numerical Simulation, 64:821--824.
[16] Shi, P., Luan, X., Liu, F. (2012). H-Inf filtering for discrete-time systems with stochastic incomplete measurement and mixed delays, IEEE Trans on Industrial Electronics, 59:2732--2739 doi:10.1109/TIE.2011.2167894
[17] Song, B., Xu, S., Zou, Y. (2009). Non-fragile H-Inf filtering for uncertain stochastic time-delay systems, International Journal of Innovative Computing, Information and Control, 5:2257--2266.
[18] Sun, Y. (2009). Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity, Physics Letters A, 373:3273--3276 doi:10.1016/j.physleta.2009.07.025
[19] Wu, Y., Zhou, X., Chen, J., Hui, B. (2009). Chaos synchronization of a new 3D chaotic system, Chaos, Solitons and Fractals, 42:1812--1819 doi:10.1016/j.chaos.2009.03.092
[20] Yang, R., Shi, P., Liu, G. (2011). Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts, IEEE Trans on Automatic Control, 56:2655--2660 doi:10.1109/TAC.2011.2166729
[21] Yang, R., Shi, P., Liu, G., Gao, H. (2011). Network-based feedback control for systems with mixed delays based on quantization and dropout compensation, Automatica, 47:2805--2809 doi:10.1016/j.automatica.2011.09.007
[22] Zhang, L. Shi, P. (2009). L2-gain and asynchronous H-Inf control of discrete-time switched systems with average dwell time, IEEE Trans on Automatic Control, 54:2193--2200 doi:10.1109/TAC.2009.2026841
[23] Zhang, L., Shi, P., Boukas, E., Wang, C. (2008). H-Inf model reduction for switched linear discrete-time systems with polytopic uncertainties, Automatica, 44:2944--2949 doi:10.1016/j.automatica.2008.03.025


BibTeX:
@article{MIC-2012-1-3,
  title={{H-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input}},
  author={Wang, Bo and Shi, Peng and Karimi, Hamid Reza and Wang, Jun},
  journal={Modeling, Identification and Control},
  volume={33},
  number={1},
  pages={27--34},
  year={2012},
  doi={10.4173/mic.2012.1.3},
  publisher={Norwegian Society of Automatic Control}
};