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In this paper, the H∞ synchronization of general chaotic systems with random perturbations is investigated, in which perturbation is a random process of Brownian motion. Based on stochastic Lyapunov stability theory, linear matrix inequalities, and It formula and H∞ control method combined with feedback control laws, some new asymptotic synchronization schemes are established which guarantee robust stochastical mean square asymptotical synchronization for drive system and noise-perturbed response system, as well as achieving a prescribed stochastic robust H∞ performance level. These schemes are in a simple form and easy to work with Matlab. Finally, simulations show that the proposed results are correct and effective.
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Keywords:
- random perturbation /
- H∞ synchronization /
- linear matrix inequalities /
- It formula
[1] Ott E, Grebogi C, Yorke J A 1990 Phys. Lett. 64 1196
[2] Pecora L M, Carroll T L 1990 Phys.Rec.Let. 64 821
[3] Tu L L, Lu J A 2005 Chin. Phys. 14 1755
[4] 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 56 6230]
[5] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 54 3502]
[6] Zhang H B, Yu Y B, Zhang J 2010 Chin. Phys. B 19 080509-1
[7] Chen G R, Lv J H 2003 Dynamics analysis, control and synchronization of Lorenz system family (Beijing: Science Press) p2 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2页]
[8] Chen G, Dong X 1998 From chaos to order:Methodologies, Perspectives and Application (Singapore: World Scientifi) p4
[9] Lorenz E N 1963 J. Atmos. Sci. 20 130
[10] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-Ⅰ 33 1072
[11] Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465
[12] Lü J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659
[13] Liu C X, Liu T, Liu L, Liu K 2004 Chaos, Solitons and Fractals 22 1031
[14] Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 55 6261]
[15] Liu Y Z, Jiang C S, Lin C S 2008 Acta Phys. Sin. 57 6808 (in Chinese) [刘扬正、姜长生、林长圣 2008 57 6808]
[16] Chen G P, Hao J B 2008 Communications Technology 41 230 (in Chinese)[陈光平、郝加波 2008 通信技术 41 230]
[17] Chen A M, Lu J A, Lv J H 2006 Physics A 364 103
[18] Zames G 1981 IEEE Trans. Automatic Control 26 301
[19] Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏 荣、王行愚 2004 53 3298]
[20] Yan J J 2004 Chaos, Solitons and Fractals 21 283
[21] Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81
[22] Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese) [杨东升、张化光、赵 琰、宋崇辉、王迎春 2010 59 1562]
[23] Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170
[24] Anton S 1992 The H∞ Control Problem (New York: Prentice-Hall) p5
[25] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System
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[1] Ott E, Grebogi C, Yorke J A 1990 Phys. Lett. 64 1196
[2] Pecora L M, Carroll T L 1990 Phys.Rec.Let. 64 821
[3] Tu L L, Lu J A 2005 Chin. Phys. 14 1755
[4] 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 56 6230]
[5] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 54 3502]
[6] Zhang H B, Yu Y B, Zhang J 2010 Chin. Phys. B 19 080509-1
[7] Chen G R, Lv J H 2003 Dynamics analysis, control and synchronization of Lorenz system family (Beijing: Science Press) p2 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2页]
[8] Chen G, Dong X 1998 From chaos to order:Methodologies, Perspectives and Application (Singapore: World Scientifi) p4
[9] Lorenz E N 1963 J. Atmos. Sci. 20 130
[10] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-Ⅰ 33 1072
[11] Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465
[12] Lü J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659
[13] Liu C X, Liu T, Liu L, Liu K 2004 Chaos, Solitons and Fractals 22 1031
[14] Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 55 6261]
[15] Liu Y Z, Jiang C S, Lin C S 2008 Acta Phys. Sin. 57 6808 (in Chinese) [刘扬正、姜长生、林长圣 2008 57 6808]
[16] Chen G P, Hao J B 2008 Communications Technology 41 230 (in Chinese)[陈光平、郝加波 2008 通信技术 41 230]
[17] Chen A M, Lu J A, Lv J H 2006 Physics A 364 103
[18] Zames G 1981 IEEE Trans. Automatic Control 26 301
[19] Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏 荣、王行愚 2004 53 3298]
[20] Yan J J 2004 Chaos, Solitons and Fractals 21 283
[21] Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81
[22] Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese) [杨东升、张化光、赵 琰、宋崇辉、王迎春 2010 59 1562]
[23] Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170
[24] Anton S 1992 The H∞ Control Problem (New York: Prentice-Hall) p5
[25] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System
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