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The synchronization problem of two time-varying delayed chaotic systems with unknown parameters is studied. A novel fuzzy adaptive H∞ control method is proposed to realize the synchronization of two time-varying delayed chaotic systems based on Lyapunov functional theory and linear matrix inequality techniques. The sufficient criterion for the stability of the synchronization error system is presented. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
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Keywords:
- time-varying delayed chaotic system /
- chaos synchronization /
- fuzzy adaptive control /
- linear matrix inequality （LMI）
[1] ［1］Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] ［2］Yan S L 2005 Acta Phys. Sin. 54 1098 （in Chinese）［颜森林 2005 54 1098］
[3] ［3］Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[4] ［4］Li N, Li J F 2008 Acta Phys. Sin. 57 6093（in Chinese）［李农、李建芬 2008 57 6093］
[5] ［5］Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[6] ［6］Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 （in Chinese）［王兴元、王明军 2007 56 5136］
[7] ［7］Wang X Y, He Y J 2008 Acta Phys. Sin. 57 1485 （in Chinese）［王兴元、贺毅杰 2007 57 1485］
[8] ［8］Yang D S, Zhang H G, Li A P, Meng Z Y 2007 Acta Phys. Sin. 56 3121 （in Chinese）［杨东升、张化光、李爱平、孟子怡 2007 56 3121］
[9] ［9］Liu Y F, Yang X G, Miao D, Yuan R P 2007 Acta Phys. Sin. 56 6250 （in Chinese）［刘云峰、杨小冈、缪栋、袁润平2007 56 6250］
[10] ］Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[11] ］Meng J, Wang X Y 2009 Acta Phys. Sin. 58 819 （in Chinese）［孟娟、王兴元 2009 58 819］
[12] ］Wang X Y, Meng J 2009 Acta Phys. Sin. 58 3780 （in Chinese）［王兴元、孟娟 2009 58 3780］
[13] ］Kim J H, Shin H, Kim E, Park M 2005 Int. J. Bifur. & Chaos 15 2593
[14] ］Zhou J, Chen T P, Xiang L 2006 Chaos, Solit. & Fract. 27 905
[15] ］Qi W, Wang Y H 2009 Chin. Phys. B 18 1404
[16] ］Wu R C 2009 Acta Phys. Sin. 58 139 （in Chinese）［吴然超 2009 58 139］
[17] ］Li T, Fei S M, Zhang K J 2008 Physica A 387 982
[18] ］Li D, Zheng Z G 2008 Chin. Phys. B 17 4009
[19] ］Ma T D, Zhang H G 2008 Chin. Phys. B 17 4407
[20] ］Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 11467 （in Chinese）［王明军、王兴元 2009 58 1467］
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[1] ［1］Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] ［2］Yan S L 2005 Acta Phys. Sin. 54 1098 （in Chinese）［颜森林 2005 54 1098］
[3] ［3］Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[4] ［4］Li N, Li J F 2008 Acta Phys. Sin. 57 6093（in Chinese）［李农、李建芬 2008 57 6093］
[5] ［5］Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[6] ［6］Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 （in Chinese）［王兴元、王明军 2007 56 5136］
[7] ［7］Wang X Y, He Y J 2008 Acta Phys. Sin. 57 1485 （in Chinese）［王兴元、贺毅杰 2007 57 1485］
[8] ［8］Yang D S, Zhang H G, Li A P, Meng Z Y 2007 Acta Phys. Sin. 56 3121 （in Chinese）［杨东升、张化光、李爱平、孟子怡 2007 56 3121］
[9] ［9］Liu Y F, Yang X G, Miao D, Yuan R P 2007 Acta Phys. Sin. 56 6250 （in Chinese）［刘云峰、杨小冈、缪栋、袁润平2007 56 6250］
[10] ］Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[11] ］Meng J, Wang X Y 2009 Acta Phys. Sin. 58 819 （in Chinese）［孟娟、王兴元 2009 58 819］
[12] ］Wang X Y, Meng J 2009 Acta Phys. Sin. 58 3780 （in Chinese）［王兴元、孟娟 2009 58 3780］
[13] ］Kim J H, Shin H, Kim E, Park M 2005 Int. J. Bifur. & Chaos 15 2593
[14] ］Zhou J, Chen T P, Xiang L 2006 Chaos, Solit. & Fract. 27 905
[15] ］Qi W, Wang Y H 2009 Chin. Phys. B 18 1404
[16] ］Wu R C 2009 Acta Phys. Sin. 58 139 （in Chinese）［吴然超 2009 58 139］
[17] ］Li T, Fei S M, Zhang K J 2008 Physica A 387 982
[18] ］Li D, Zheng Z G 2008 Chin. Phys. B 17 4009
[19] ］Ma T D, Zhang H G 2008 Chin. Phys. B 17 4407
[20] ］Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 11467 （in Chinese）［王明军、王兴元 2009 58 1467］
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