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In this paper, an stability theorem is proposed for a fractional state space system based on Lyapunov stability theory. Controller can be achieved easily by this theory without calculating any equilibrium point. The fractional unified chaotic system is used to improve the stability theorem. The effectiveness of the theory is verified by the simulation results.
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Keywords:
- fractional-order /
- state space system /
- stability /
- unified chaotic systems
[1] Chen J R, Tao R J 2001 Journal of Shanghai University 5 292
[2] Abbisso S, Caponetto R 2001 ISCAS 2001, Ⅲ—688
[3] Wang F P, Guo J B, Wang Z J, Xiao D C, Li M T 2001 Acta Phys. Sin. 50 1019 (in Chinese) [汪芙平、 郭静波、 王赞基、 萧达川、 李茂堂 2001 50 1019]
[4] Cui B T, Lou X Y 2008 Chin. Phys. B 17 520
[5] Cui B T, Ji Y, Qiu F 2009 Chin. Phys. B 18 5203
[6] Wang F P, Wang Z J, Guo J B 2002 Acta Phys. Sin. 51 474 (in Chinese) [汪芙平、 王赞基、 郭静波 2002 51 474]
[7] Hubler A, Helv 1989 Phys. Acta 62 343
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett., 64 1196
[9] Lu J A, Zhang Q J 2008 Chin. Phys. B 17 492
[10] Wu Z Q, Yue D, Xu S F 2002 Acta Phys. Sin. 51 1193 (in Chinese) [吴忠强、 岳 东、 许世范 2002 51 1193]
[11] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高 心、 刘兴文 2007 56 84]
[12] Gu C M, Shen K 1998 Acta Phys. Sin. 47 732 (in Chinese) [顾春明、 沈 柯 1998 47 732]
[13] Yu H J 2005 Acta Phys. Sin 54 5044 (in Chinese) [于洪洁 2005 54 5044] 〖14] Hunt E R 1991 Phys. Rev. Lett. 67 1953
[14] Pyragas K 1992 Phys. Lett. A 170 421
[15] Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[16] Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[17] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[18] Hu G, He K F 1993 Phys. Rev. Lett. 71 3794
[19] Auerbach D 1994 Phys. Rev. Lett. 72 1184
[20] Hu G, Xiao J H, Gao J H 2000 Phys. Rev. E 62 3043
[21] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press)
[22] Matignon D 1996 IMACS, IEEE2SMC, Lille, France 963
[23] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵、 韩 焱、 赵灵冬 2009 58 2235]
[24] Mohammad S T, Mohammad H 2007 Physics Letters A 367 102
[25] Zhou P 2008 Chin. Phys. B 17 3252
[26] Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
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[1] Chen J R, Tao R J 2001 Journal of Shanghai University 5 292
[2] Abbisso S, Caponetto R 2001 ISCAS 2001, Ⅲ—688
[3] Wang F P, Guo J B, Wang Z J, Xiao D C, Li M T 2001 Acta Phys. Sin. 50 1019 (in Chinese) [汪芙平、 郭静波、 王赞基、 萧达川、 李茂堂 2001 50 1019]
[4] Cui B T, Lou X Y 2008 Chin. Phys. B 17 520
[5] Cui B T, Ji Y, Qiu F 2009 Chin. Phys. B 18 5203
[6] Wang F P, Wang Z J, Guo J B 2002 Acta Phys. Sin. 51 474 (in Chinese) [汪芙平、 王赞基、 郭静波 2002 51 474]
[7] Hubler A, Helv 1989 Phys. Acta 62 343
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett., 64 1196
[9] Lu J A, Zhang Q J 2008 Chin. Phys. B 17 492
[10] Wu Z Q, Yue D, Xu S F 2002 Acta Phys. Sin. 51 1193 (in Chinese) [吴忠强、 岳 东、 许世范 2002 51 1193]
[11] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高 心、 刘兴文 2007 56 84]
[12] Gu C M, Shen K 1998 Acta Phys. Sin. 47 732 (in Chinese) [顾春明、 沈 柯 1998 47 732]
[13] Yu H J 2005 Acta Phys. Sin 54 5044 (in Chinese) [于洪洁 2005 54 5044] 〖14] Hunt E R 1991 Phys. Rev. Lett. 67 1953
[14] Pyragas K 1992 Phys. Lett. A 170 421
[15] Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[16] Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[17] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[18] Hu G, He K F 1993 Phys. Rev. Lett. 71 3794
[19] Auerbach D 1994 Phys. Rev. Lett. 72 1184
[20] Hu G, Xiao J H, Gao J H 2000 Phys. Rev. E 62 3043
[21] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press)
[22] Matignon D 1996 IMACS, IEEE2SMC, Lille, France 963
[23] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵、 韩 焱、 赵灵冬 2009 58 2235]
[24] Mohammad S T, Mohammad H 2007 Physics Letters A 367 102
[25] Zhou P 2008 Chin. Phys. B 17 3252
[26] Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
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