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Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control. (English) Zbl 1201.93045
Summary: This paper investigates the global synchronization of a class of third-order non-autonomous chaotic systems via the master-slave linear state error feedback control. A sufficient global synchronization criterion of linear matrix inequality (LMI) and several algebraic synchronization criteria for single-variable coupling are proven. These LMI and algebraic synchronization criteria are then applied to two classes of well-known third-order chaotic systems, the generalized Lorenz systems and the gyrostat systems, proving that the local synchronization criteria for the chaotic generalized Lorenz systems developed in the existing literature can actually be extended to describe global synchronization and obtaining some easily implemented synchronization criteria for the gyrostat systems.
MSC:
93B52Feedback control
34D06Synchronization
37D45Strange attractors, chaotic dynamics
37N35Dynamical systems in control
References:
[1]Lakshmanman, M.; Murali, K.: Chaos in nonlinear oscillators: controlling and synchronization, (1996)
[2]Blasius, B.; Huppert, A.; Stone, L.: Complex dynamics and phase synchronization in spatially extended ecological system, Nature 399, 354-359 (1999)
[3]Mu, X.; Pei, L.: Synchronization of the near-identical chaotic systems with the unknown parameters, Appl. math. Model. 34, 1788-1797 (2010) · Zbl 1193.37046 · doi:10.1016/j.apm.2009.09.023
[4]Ge, Z. M.; Lin, T. N.: Chaos, chaos control and synchronization of a gyrostat system, J. sound vib. 251, 519-542 (2002)
[5]Jiang, G. P.; Tang, W. K. S.: A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach, Int. J. Bifurcat. chaos 12, 2239-2253 (2002) · Zbl 1052.34053 · doi:10.1142/S0218127402005790
[6]Jiang, G. P.; Chen, G.; Tang, W. K. S.: A new criterion for chaos synchronization using linear state feedback control, Int. J. Bifurcat. chaos 13, No. 8, 2343-2351 (2003) · Zbl 1064.37515 · doi:10.1142/S0218127403008004
[7]Jiang, G. P.; Tang, W. K. S.; Chen, G.: A simple global synchronization criterion for coupled chaotic systems, Chaos soliton fract. 15, 925-935 (2003) · Zbl 1065.70015 · doi:10.1016/S0960-0779(02)00214-X
[8]Sun, J.; Zhang, Y.: Some simple global synchronization criterions for coupled time-varied chaotic systems, Chaos soliton fract. 19, 93-98 (2004) · Zbl 1069.34068 · doi:10.1016/S0960-0779(03)00083-3
[9]Ge, Z. M.; Chang, C. M.: Chaos synchronization and parameters identification of single time scale brushless DC motors, Chaos soliton fract. 20, 883-903 (2004) · Zbl 1071.34048 · doi:10.1016/j.chaos.2003.10.005
[10]Ge, Z. M.; Leu, W. Y.: Chaos synchronization and parameter identification for loudspeaker systems, Chaos soliton fract. 21, 1231-1247 (2004) · Zbl 1060.93523 · doi:10.1016/j.chaos.2003.12.062
[11]Ge, Z. M.; Cheng, J. W.: Chaos synchronization and parameter identification of three time scales brushless DC motor system, Chaos soliton fract. 24, 597-616 (2005) · Zbl 1061.93524 · doi:10.1016/j.chaos.2004.09.031
[12]Haeri, M.; Khademian, B.: Comparison between different synchronization methods of identical chaotic systems, Chaos soliton fract. 29, 1002-1022 (2006) · Zbl 1142.37326 · doi:10.1016/j.chaos.2005.08.101
[13]Chen, H. H.: Global synchronization of chaotic systems via linear balanced feedback control, Appl. math. Comput. 186, 923-931 (2007) · Zbl 1113.93047 · doi:10.1016/j.amc.2006.08.017
[14]Mahmoud, G. M.; Aly, S. A.; Farghaly, A. A.: On chaos synchronization of a complex two coupled dynamos system, Chaos soliton fract. 33, 178-187 (2007)
[15]Wu, X.; Chen, G.; Cai, J.: Chaos synchronization of the master – slave generalized Lorenz systems via linear state error feedback control, Physica D 229, 52-80 (2007)
[16]Sarasola, C.; Torrealdea, F. J.; Anjou, A. D.; Moujahid, A.; Grana, M.: Feedback synchronization of chaotic systems, Int. J. Bifurcat. chaos 13, No. 1, 177-191 (2008)
[17]Wang, F.; Liu, C.: A new criterion for chaos and hyperchaos synchronization using linear feedback control, Phys. lett. A 360, 274-278 (2006)
[18]Han, X.; Lu, J. A.; Wu, X.: Adaptive feedback synchronization of Lü system, Chaos soliton fract. 22, 221-227 (2004) · Zbl 1060.93524 · doi:10.1016/j.chaos.2003.12.103
[19]Yassen, M. T.: Controlling chaos and synchronization for new chaotic system using linear feedback control, Chaos soliton fract. 26, 913-920 (2005) · Zbl 1093.93539 · doi:10.1016/j.chaos.2005.01.047
[20]Wu, X. F.; Zhao, Y.: Frequency domain criterion for chaos synchronization of Lur’e systems via linear state error feedback control, Int. J. Bifurcat. chaos 15, No. 4, 1445-1454 (2005) · Zbl 1089.93016 · doi:10.1142/S0218127405012569
[21]Liao, X.; Chen, G.; Xu, B.; Shen, Y.: On global exponential synchronization of Chua circuits, Int. J. Bifurcat. chaos 15, No. 7, 2227-2234 (2005) · Zbl 1092.93590 · doi:10.1142/S0218127405013198
[22]Wu, X.; Cai, J.; Zhao, Y.: Some new algebraic criteria for chaos synchronization of Chua’s circuits by linear state error feedback control, Int. J. Circ. theor. Appl. 34 (2006) · Zbl 1123.94012 · doi:10.1002/cta.350
[23]Wu, X.; Cai, J.; Wang, M.: Master – slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control, J. sound vib. 295, 378-387 (2006)
[24]Čelikovský, S.; Chen, G.: On a generalized Lorenz canonical form of chaotic systems, Int. J. Bifurcat. chaos 12, 1789-1812 (2002) · Zbl 1043.37023 · doi:10.1142/S0218127402005467
[25]Lü, J.; Chen, G.; Cheng, D.: A new chaotic system and beyond: the generalized Lorenz-like system, Int. J. Bifurcat. chaos 14, 1507-1537 (2004) · Zbl 1129.37323 · doi:10.1142/S021812740401014X
[26]Huang, D.; Zhang, L.: Dynamics of the Lorenz – robbins system with control, Physica D 218, 131-138 (2006) · Zbl 1108.34038 · doi:10.1016/j.physd.2006.04.016
[27]Agiza, H. N.: Chaos synchronization of two coupled dynamos systems with unknown system parameters, Int. J. Mod. phys. C 15, No. 6, 873-883 (2004) · Zbl 1082.34041 · doi:10.1142/S0129183104006303
[28]Liu, W. B.; Chen, G.: A new chaotic system and its generation, Int. J. Bifurcat. chaos 12, 261-267 (2003) · Zbl 1078.37504 · doi:10.1142/S0218127403006509
[29]Ge, Z. M.; Chang, C. M.; Chen, Y. S.: Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems, Chaos soliton fract. 27, 1298-1315 (2006) · Zbl 1091.93554 · doi:10.1016/j.chaos.2005.04.095
[30]Jia, Q.: Chaos control and synchronization of the Newton – leipnik chaotic system, Chaos soliton fract. 35, 814-824 (2008)
[31]Ge, Z. M.; Lee, C. I.; Chen, H. H.; Lee, S. C.: Non-linear dynamics and chaos control of a damped satellite with partially-filled liquid, J. sound vib. 217, 807-825 (1998)
[32]Yassen, M. T.: Adaptive control and synchronization of a modified Chua’s circuit system, Appl. math. Comput. 135, 113-128 (2003) · Zbl 1038.34041 · doi:10.1016/S0096-3003(01)00318-6
[33]Fostin, H.; Bowong, S.; Daafouz, J.: Adaptive synchronization of two chaotic systems consisting of modified van der Pol – Duffing and Chua oscillators, Chaos soliton fract. 26, 215-229 (2005) · Zbl 1122.93069 · doi:10.1016/j.chaos.2004.12.029
[34]Li, Z.; Xu, D.: Stability criterion for projective synchronization in three-dimensional chaotic systems, Phys. lett. A 282, 175-179 (2001) · Zbl 0983.37036 · doi:10.1016/S0375-9601(01)00185-2
[35]Li, Y.; Liu, X.; Zhang, H.: Dynamical analysis and impulsive control of a new hyperchaotic system, Math. comput. Model. 42, 1359-1374 (2005) · Zbl 1121.37031 · doi:10.1016/j.mcm.2004.09.011
[36]Chen, Y.; Wu, X.: Global chaos synchronization of nonautonomous gyrostat systems via variable substitution control, Int. J. Bifurcat. chaos 18, No. 12, 3719-3730 (2008) · Zbl 1165.34368 · doi:10.1142/S0218127408022676
[37]Curran, P. F.; Chua, L. O.: Absolute stability theory and the synchronization problem, Int. J. Bifurcat. chaos 7, 1357-1382 (1997) · Zbl 0910.34054 · doi:10.1142/S0218127497001096
[38]Slotine, J. E.; Li, W. P.: Applied nonlinear control, (2004)
[39]Horn, R. A.; Johnson, C. R.: Matrix analysis, (1985)