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Chaos synchronization in fractional-order unified chaotic system is disscussed in this paper. Based on the stability theory of fractional-order system, the control law is presented to achieve chaos synchronization. The advantage of the proposed controllers is that they are linear and have lower dimensions than that of the states. With this technique it is very easy to find the suitable feedback constant. Simulation results for fractional-order Lorenz, Lü and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme.
[1] ［1]Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans CAI 42 485
[2] ［2]Grigorenko I, Grigorenko E 2003 Phys.Rev. Lett. 91 034101
[3] ［3]Li C P , Peng G J 2004 Chaos, Solitons & Fractals 22 443
[4] ［4]Li C G , Chen G R 2004 Chaos, Solitons & Fractals 22 549
[5] ［5]Lu J G , Chen G R 2006 Chaos, Solitons & Fractals 27 685
[6] ［6]Deng W H, Li C P 2005 Physica A 353 61
[7] ［7]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922（in Chinese）［王发强、刘崇新 2006 物理学报 55 3922］
[8] ［8]Chen X R, Liu C X, Wang F Q,Li Y X 2008 Acta Phys. Sin. 57 1416（in Chinese）［陈向荣、刘崇新、刘发强、李永勋 2008 物理学报 57 1416］
[9] ［9]Liu C X, Liu T, Liu L， Liu K 2004 Chaos, Solitions and Fractals 22 1031
[10] ［10]Gao X, Yu J B 2005 Chaos, Solitons & Fractals 24 1097
[11] ［11]Ahamd W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[12] ［12]Gao X, Yu J B 2005 Chin. Phys. 14 908
[13] ［13]Li C G , Chen G R 2004 Physica A 341 55
[14] ［14]Liu C X 2007 Acta Phys. Sin. 56 6865（in Chinese）［刘崇新 2007 物理学报 56 6865］
[15] ［15]Arman Kiani-B, Kia Fallahi , Naser Pariz , Henry Leung 2009 Communications in Nonlinear Science and Numerical Simulation 14 863
[16] ［16]Li C P, Deng WH, 2006 Int J Modern Phys. B 20 791
[17] ［17]Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[18] ［18]Hu J B, H Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 （in Chinese）［胡建兵、韩焱、赵灵冬 2008 物理学报 57 7522］
[19] ［19]Zhang R X ,Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 （in Chinese）［张若洵、杨洋、杨世平 2009 物理学报 58 6039］
[20] ［20]Wang X Y, Song J M 2009 Communications in Nonlinear Science and Numerical Simulation, doi: 101016/j.cnsns.200901010
[21] ［21]Zhang R X, Yang S P 2008 Acta Phys. Sin. 57 6837 （in Chinese）［张若洵、 杨世平 2008 物理学报 57 6837］
[22] ［22]Lu J J, Liu C X 2007 Chin. Phys.16 1586
[23] ［23]Zhang R X, Yang S P 2009 Chin. Phys. B 18 2957
[24] ［24]Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 （in Chinese）［张若洵、 杨世平 2008 物理学报 58 2957］
[25] ［25]Caputo M. 1967 The Geophys J Roy Astronom Soc. 13 529
[26] ［26]Lü J H, Chen G R 2002 Int. J of Bifurcation and Chaos 12 659
[27] ［27]Lü J H, Chen G R Zhang S C 2002 Int. J of Bifurcation and Chaos 12 1001
[28] ［28]Wang X J, Li J, Chen G R 2008 J. of the Franklin Institute 345 392
[29] ［29]Matignon D 1996 In: IMACS, IEEE-SMC, Lille,France 963
[30] ［30]Diethelm K, Ford N J, Freed A D 2002 Nonlinear Dynamics 29 3
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[1] ［1]Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans CAI 42 485
[2] ［2]Grigorenko I, Grigorenko E 2003 Phys.Rev. Lett. 91 034101
[3] ［3]Li C P , Peng G J 2004 Chaos, Solitons & Fractals 22 443
[4] ［4]Li C G , Chen G R 2004 Chaos, Solitons & Fractals 22 549
[5] ［5]Lu J G , Chen G R 2006 Chaos, Solitons & Fractals 27 685
[6] ［6]Deng W H, Li C P 2005 Physica A 353 61
[7] ［7]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922（in Chinese）［王发强、刘崇新 2006 物理学报 55 3922］
[8] ［8]Chen X R, Liu C X, Wang F Q,Li Y X 2008 Acta Phys. Sin. 57 1416（in Chinese）［陈向荣、刘崇新、刘发强、李永勋 2008 物理学报 57 1416］
[9] ［9]Liu C X, Liu T, Liu L， Liu K 2004 Chaos, Solitions and Fractals 22 1031
[10] ［10]Gao X, Yu J B 2005 Chaos, Solitons & Fractals 24 1097
[11] ［11]Ahamd W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[12] ［12]Gao X, Yu J B 2005 Chin. Phys. 14 908
[13] ［13]Li C G , Chen G R 2004 Physica A 341 55
[14] ［14]Liu C X 2007 Acta Phys. Sin. 56 6865（in Chinese）［刘崇新 2007 物理学报 56 6865］
[15] ［15]Arman Kiani-B, Kia Fallahi , Naser Pariz , Henry Leung 2009 Communications in Nonlinear Science and Numerical Simulation 14 863
[16] ［16]Li C P, Deng WH, 2006 Int J Modern Phys. B 20 791
[17] ［17]Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[18] ［18]Hu J B, H Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 （in Chinese）［胡建兵、韩焱、赵灵冬 2008 物理学报 57 7522］
[19] ［19]Zhang R X ,Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 （in Chinese）［张若洵、杨洋、杨世平 2009 物理学报 58 6039］
[20] ［20]Wang X Y, Song J M 2009 Communications in Nonlinear Science and Numerical Simulation, doi: 101016/j.cnsns.200901010
[21] ［21]Zhang R X, Yang S P 2008 Acta Phys. Sin. 57 6837 （in Chinese）［张若洵、 杨世平 2008 物理学报 57 6837］
[22] ［22]Lu J J, Liu C X 2007 Chin. Phys.16 1586
[23] ［23]Zhang R X, Yang S P 2009 Chin. Phys. B 18 2957
[24] ［24]Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 （in Chinese）［张若洵、 杨世平 2008 物理学报 58 2957］
[25] ［25]Caputo M. 1967 The Geophys J Roy Astronom Soc. 13 529
[26] ［26]Lü J H, Chen G R 2002 Int. J of Bifurcation and Chaos 12 659
[27] ［27]Lü J H, Chen G R Zhang S C 2002 Int. J of Bifurcation and Chaos 12 1001
[28] ［28]Wang X J, Li J, Chen G R 2008 J. of the Franklin Institute 345 392
[29] ［29]Matignon D 1996 In: IMACS, IEEE-SMC, Lille,France 963
[30] ［30]Diethelm K, Ford N J, Freed A D 2002 Nonlinear Dynamics 29 3
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