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By analyzing structural characteristics of nonlinear vector field for a class of chaotic systems, a new approach to controlling chaos globally and rapidly is put forward. Based on linear state feedback, an independent stable equation of some state variables is separated. Controlled chaotic systems degenerate gradually into stable linear systems. Nonlinear quivering phenomenon is eliminated completely further. The approach can be used to control Lorenz system families or new chaotic systems with similar structures. A class of simple controllers is designed to guarantee that closed-loop systems are globally asymptotically stable at the origin. Numerical examples illustrate the shortcut and the validity of the presented approach in this paper.
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Keywords:
- chaotic systems /
- linear state feedback /
- global stabilization
[1] Tavazoei M S, Haeri M 2008 Phys. Lett. A 372 798
[2] Liu D B, Yang X S 2008 Chaos, Soliton. Fract. 36 709
[3] Gomes A A, Manica E, Varriale M C 2008 Chaos, Soliton. Fract. 36 1097
[4] Wan C J, Bernstein D S 1995 Dynam. Contr. 5 321
[5] Lü J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[6] Li W L, Chen X Q, Shen Z P 2008 Chin. Phys. B 17 87
[7] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549(in Chinese)[张若洵、杨世平、刘永利 2010 物理学报 59 1549 ]
[8] Liu M H, Feng J C 2009 Acta Phys. Sin. 58 4457(in Chinese)[刘明华、冯久超 2009 物理学报 58 4457]
[9] Zhou P, Cheng X F, Zhang N Y 2008 Acta Phys. Sin. 57 5407(in Chinese)[周 平、程雪峰、张年英 2008 物理学报 57 5407]
[10] Zhou P, Wei L J, Cheng X F 2009 Acta Phys. Sin. 58 5201(in Chinese)[周 平、危丽佳、程雪峰 2009 物理学报 58 5201]
[11] Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[12] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136(in Chinese)[王兴元、王明军 2007 物理学报 56 5136]
[13] Li R H, Xu W, Li S 2006 Acta Phys. Sin. 55 598(in Chinese)[李瑞红、徐 伟、李 爽 2006 物理学报 55 598]
[14] Li N, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404(in Chinese)[李 农、李建芬、刘宇平、马健 2008 物理学报 57 1404]
[15] Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese)[许 喆、刘崇新、杨 韬 2010物理学报 59 1524]
[16] Wu R C, Guo Y X 2010 Acta Phys. Sin. 59 5293(in Chinese)[吴然超、郭玉祥 2010 物理学报 59 5293]
[17] Jiang F, Liu Z, Hu W, Bao B C 2010 Acta Phys. Sin. 59 116(in Chinese)[蒋 飞、刘 中、胡 文、包伯成 2010 物理学报 59 116]
[18] Zhu S P, Qian F C, Liu D 2010 Acta Phys. Sin. 59 2250 (in Chinese)[朱少平、钱富才、刘 丁 2010 物理学报 59 2250]
[19] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147(in Chinese)[张化光、马大中、王占山、冯 健 2010 物理学报 59 147]
[20] Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230(in Chinese)[蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]
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[1] Tavazoei M S, Haeri M 2008 Phys. Lett. A 372 798
[2] Liu D B, Yang X S 2008 Chaos, Soliton. Fract. 36 709
[3] Gomes A A, Manica E, Varriale M C 2008 Chaos, Soliton. Fract. 36 1097
[4] Wan C J, Bernstein D S 1995 Dynam. Contr. 5 321
[5] Lü J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[6] Li W L, Chen X Q, Shen Z P 2008 Chin. Phys. B 17 87
[7] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549(in Chinese)[张若洵、杨世平、刘永利 2010 物理学报 59 1549 ]
[8] Liu M H, Feng J C 2009 Acta Phys. Sin. 58 4457(in Chinese)[刘明华、冯久超 2009 物理学报 58 4457]
[9] Zhou P, Cheng X F, Zhang N Y 2008 Acta Phys. Sin. 57 5407(in Chinese)[周 平、程雪峰、张年英 2008 物理学报 57 5407]
[10] Zhou P, Wei L J, Cheng X F 2009 Acta Phys. Sin. 58 5201(in Chinese)[周 平、危丽佳、程雪峰 2009 物理学报 58 5201]
[11] Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[12] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136(in Chinese)[王兴元、王明军 2007 物理学报 56 5136]
[13] Li R H, Xu W, Li S 2006 Acta Phys. Sin. 55 598(in Chinese)[李瑞红、徐 伟、李 爽 2006 物理学报 55 598]
[14] Li N, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404(in Chinese)[李 农、李建芬、刘宇平、马健 2008 物理学报 57 1404]
[15] Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese)[许 喆、刘崇新、杨 韬 2010物理学报 59 1524]
[16] Wu R C, Guo Y X 2010 Acta Phys. Sin. 59 5293(in Chinese)[吴然超、郭玉祥 2010 物理学报 59 5293]
[17] Jiang F, Liu Z, Hu W, Bao B C 2010 Acta Phys. Sin. 59 116(in Chinese)[蒋 飞、刘 中、胡 文、包伯成 2010 物理学报 59 116]
[18] Zhu S P, Qian F C, Liu D 2010 Acta Phys. Sin. 59 2250 (in Chinese)[朱少平、钱富才、刘 丁 2010 物理学报 59 2250]
[19] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147(in Chinese)[张化光、马大中、王占山、冯 健 2010 物理学报 59 147]
[20] Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230(in Chinese)[蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]
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