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Synchronization of fractional chaotic systems based on fractional-order interval systems

Sun Ning

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Synchronization of fractional chaotic systems based on fractional-order interval systems

Sun Ning
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  • Synchronization of fractional-order chaotic systems is investigated by designing a novel nonlinear feedback controller. Compared with the previous reports, the controlled synchronization error system does not need to turn into a linear system and the performance is improved effectively. Furthermore, a novel sufficient stabilization criterion for fractional-order chaotic systems is proposed by introducing a stabilization criterion of an interval fractional-order linear time-invariant system and using the linear matrix inequality technique. Consequently, the chaotic synchronization is ensured. The simulation result verifies the effectiveness of the proposed method.
    [1]

    Zhu H, Zhou S, Zhang J 2009 Chaos Soliton Fract. 39 1595

    [2]

    Li C, Peng G 2004 Chaos Soliton Fract. 22 443

    [3]

    Lu J G 2006 Phys. Lett. A 354 305

    [4]

    Xu C, Feng J W, Austin F, Zhang W Q 2009 Int. J. Nonlin. Sci. Numer. Simul. 10 1517

    [5]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [6]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742

    [7]

    Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization and Chaotification (New York:Springer Verlag) p38

    [8]

    Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlin. Sci. Numer. Simul. 15 3536

    [9]

    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]

    [10]

    Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周 平、邝 菲 2010 物理学报 59 6851]

    [11]

    Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509

    [12]

    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]

    [13]

    Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙 宁、张化光、王智良 2011 物理学报 60 050511]

    [14]

    Lu J G, Chen G R 2009 IEEE Trans. Aut. Contr. 54 1294

    [15]

    Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p18

    [16]

    Matignon D 1996 Computational Engineering in System Application (Lille: IEEE) p963

    [17]

    Moze M, Sabatier J, Oustaloup A 2005 Proceedings of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Long Beach: ASME) p1611

    [18]

    Khargonekar P P, Petersen I R, Zhou K 1990 IEEE Trans. Autom. Control 35 356

    [19]

    Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM) p7

  • [1]

    Zhu H, Zhou S, Zhang J 2009 Chaos Soliton Fract. 39 1595

    [2]

    Li C, Peng G 2004 Chaos Soliton Fract. 22 443

    [3]

    Lu J G 2006 Phys. Lett. A 354 305

    [4]

    Xu C, Feng J W, Austin F, Zhang W Q 2009 Int. J. Nonlin. Sci. Numer. Simul. 10 1517

    [5]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [6]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742

    [7]

    Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization and Chaotification (New York:Springer Verlag) p38

    [8]

    Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlin. Sci. Numer. Simul. 15 3536

    [9]

    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]

    [10]

    Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周 平、邝 菲 2010 物理学报 59 6851]

    [11]

    Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509

    [12]

    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]

    [13]

    Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙 宁、张化光、王智良 2011 物理学报 60 050511]

    [14]

    Lu J G, Chen G R 2009 IEEE Trans. Aut. Contr. 54 1294

    [15]

    Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p18

    [16]

    Matignon D 1996 Computational Engineering in System Application (Lille: IEEE) p963

    [17]

    Moze M, Sabatier J, Oustaloup A 2005 Proceedings of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Long Beach: ASME) p1611

    [18]

    Khargonekar P P, Petersen I R, Zhou K 1990 IEEE Trans. Autom. Control 35 356

    [19]

    Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM) p7

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Publishing process
  • Received Date:  03 March 2011
  • Accepted Date:  01 July 2011
  • Published Online:  05 June 2011

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