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In the paper, the finite-time stability control problem for the Lorenz chaos system is studied. Considering the existence of uncertainty and nonlinearity in the Lorenz chaos system, a control method is proposed, which makes the controlled Lorenz system achieve approximate finite-time stability. And one kind of extended state observer is improved and designed to solve the unknown problem of uncertainty and nonlinearity for the controlled Lorenz system. The approximate finite-time stability of the closed-loop system is analysed by introducing the singular perturbation theary. Simulation results show the effectiveness of the control method and observer.
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Keywords:
- Lorenz chaos system /
- approximate finite-time stable /
- extended state observer /
- singular perturbation
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[32] Sanjay P B, Dennis S B 2005 Math.Control Signals Systems 17 101
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[42] [43] Kokotovic P,Hassan K 1986 Singular Perturbation Methods in control Analysis and Design(London:Academic Press, SIAM) P136
[44] [45] Zheng D Z 2002 Linear System Theory(2st ed)(Beijing: Tsinghua University Press) P238 (in Chinese) [郑大钟 2002 线性系统理论(第二版)(北京:清华大学出版社) 第238页]
[46] [47] Zhang K Y,Xu Z,Lu Q 2001 MATRIX THEARY(1st ed)(Xi an:Northwestern Polytechnical University Press) P83 (in Chinese)[张凯院、徐 仲、陆全 2001 矩阵论(第一版)(西安:西北工业大学出版社) 第83页]
[48] Andrea B,Lionel R 2005 Liapunov Functions and Stability in Control Theary(2st ed)(Springer-Verlag Berlin Heidelberg) P175
[49] -
[1] Chen G R, L J H 2003 Dynamics Analysis,Control and Synchronization for Lorenz system families (1st ed)(Beijing: Science press) P1,P4(in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步(第一版)(北京:科学出版社) 第1页、第4页]
[2] Yu J Z,Su N, Vincent T L 1998 Acta Phys.Sin. 47 P0397(in Chinese)[余建祖、苏 楠 1998 物理学报 47 P0397]
[3] [4] Tang G N,Luo X S,Kong L J 2000 Acta Phys.Sin. 49 0030(in Chinese)[唐国宁、罗晓曙、孔令江 2000 物理学报 49 0030]
[5] [6] Chen M Y,Zhou D H,Shang Y 2004 Chaos,Solitions and Fractals 21 P295
[7] [8] [9] Chen G P,Hao J B 2009 Acta Phys.Sin. 58 2914(in Chinese)[陈光平、郝加波 2009 物理学报 58 2914]
[10] [11] Cai G L,Zheng S, Tian L X 2008 Chin.Phys. B 17 2412
[12] [13] Li S H, Tian Y P 2003 Chin.Phys. 12 P590
[14] [15] Wang Y N,Tan W,Duan F 2006 Chin.Phys. 15 P89
[16] Qi D L,Wang Q,Gu H 2008 Chin.Phys. B 17 P847
[17] [18] [19] Wang C, Ge S S 2001 International Journal of Bifurcation and Chaos 11 1115
[20] Pishkenari H N, Meghdari A 2008 Proceeding of the 5th International Symposium on Mechatronics and its Applications (ISMA08) 8 4244
[21] [22] Bai E W,Karl E L 2000 Chaos,Solitons and Fractals 11 1041
[23] [24] [25] Guo H J,Liu J H 2004 Acta Phys.Sin. 53 4080(in Chinese)[郭会军、刘君华 2004 物理学报 53 4080]
[26] [27] Yang S K,Chen C L,Yau H T 2002 Chaos, Solitons and Fractals 13 767
[28] [29] Yau H T,Yan J J 2004 Chao,Solition and Fractals 19 891
[30] [31] Zhang H,Ma X K, Liu W Z 2004 Chaos,Solitons and Fractals 21 1249
[32] Sanjay P B, Dennis S B 2005 Math.Control Signals Systems 17 101
[33] [34] Ahmad N A, Hassan K K.A 1999 IEEE Transactions on Automatic Control 44 1672
[35] [36] [37] Zheng Q,Gao L Q, Gao Z Q 2007 Proceedings of the 46th IEEE Conference on Decision and Control ThB07.6 3501
[38] Hassan K K 2007 Nonlinear Systems(3st ed)(Beijing:Publishing House of Electronics Industry) P613
[39] [40] [41] Hassan K K 2008 International Conference on Control,Automation and Systems xlvii lvii
[42] [43] Kokotovic P,Hassan K 1986 Singular Perturbation Methods in control Analysis and Design(London:Academic Press, SIAM) P136
[44] [45] Zheng D Z 2002 Linear System Theory(2st ed)(Beijing: Tsinghua University Press) P238 (in Chinese) [郑大钟 2002 线性系统理论(第二版)(北京:清华大学出版社) 第238页]
[46] [47] Zhang K Y,Xu Z,Lu Q 2001 MATRIX THEARY(1st ed)(Xi an:Northwestern Polytechnical University Press) P83 (in Chinese)[张凯院、徐 仲、陆全 2001 矩阵论(第一版)(西安:西北工业大学出版社) 第83页]
[48] Andrea B,Lionel R 2005 Liapunov Functions and Stability in Control Theary(2st ed)(Springer-Verlag Berlin Heidelberg) P175
[49]
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