Stochastic linear generalized synchronization of chaotic systems via robust control. (English) Zbl 1220.37021
Summary: In this Letter, based on robust control, we provide a general theoretical result on stochastic linear generalized synchronization (GS) of chaotic systems. Given a driving system with noise perturbations and a linear synchronization function, a response system is developed easily according to the scheme derived here. By introducing the Lyapunov stability theory and linear matrix inequalities (LMIs), the condition for synchronization is proved to be effective. Finally, the Lorenz system is taken for illustration and verification.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37N35 | Dynamical systems in control |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 93C40 | Adaptive control/observation systems |
References:
| [1] | Bowong, S., Phys. Lett. A, 326, 1, 102 (2004) · Zbl 1161.94389 |
| [2] | Bowong, S.; Kakmeni, F. M.M.; Fotsin, H., Phys. Lett. A, 355, 3, 193 (2006) |
| [3] | Lu, J. A.; Wu, X. Q.; Lü, J. H., Phys. Lett. A, 305, 6, 365 (2002) |
| [4] | Wang, Q. Y.; Lu, Q. S.; Chen, G. R., Phys. Lett. A, 356, 1, 17 (2006) · Zbl 1160.81304 |
| [5] | Shuai, J. W.; Durand, D. M., Phys. Lett. A, 264, 4, 289 (1999) · Zbl 0949.37015 |
| [6] | Lu, J. Q.; Cao, J. D., Physics A: Stat. Mech. Appl., 382, 2, 672 (2007) |
| [7] | Cao, J.; Chen, G.; Li, P., IEEE Trans. Syst. Man Cybern. B: Cybernetics, 38, 2, 488 (2008) |
| [8] | Yu, W.; Cao, J.; Lu, J., SIAM J. Appl. Dynam. Syst., 7, 1, 108 (2008) · Zbl 1161.94011 |
| [9] | Pecora, L. M.; Carroll, T. L., Phys. Rev. Lett., 64, 8, 821 (1990) · Zbl 0938.37019 |
| [10] | Yassen, M. T., Chaos Solitons Fractals, 25, 2, 379 (2005) · Zbl 1125.93473 |
| [11] | Tang, F.; Wang, L., Phys. Lett. A, 346, 5, 342 (2005) · Zbl 1195.94105 |
| [12] | Li, P.; Cao, J., IET Control Theor. Appl., 1, 3, 795 (2007) |
| [13] | González-Miranda, J. M., Phys. Rev. E, 65, 4, 047202 (2002) |
| [14] | Uchida, A.; McAllister, R.; Meucci, R., Phys. Rev. Lett., 91, 17, 174101 (2003) |
| [15] | Rogers, E.; Kalra, R.; Schroll, R., Phys. Rev. Lett., 93, 8, 084101 (2004) |
| [16] | Huang, X.; Cao, J., Nonlinearity, 19, 12, 2797 (2006) · Zbl 1111.37022 |
| [17] | Lin, W.; Chen, G. R., Chaos, 16, 013134 (2006) · Zbl 1144.37375 |
| [18] | Hu, A. H.; Xu, Z. Y., Acta Phys. Sinica, 56, 6, 3132 (2007) · Zbl 1150.37331 |
| [19] | Zhang, Q.; Chen, S. H.; Hu, Y. M., Physica A: Stat. Theor. Phys., 371, 2, 317 (2006) |
| [20] | Haeri, M.; Tavazoei, M. S.; Naseh, M. R., Chaos Solitons Fractals, 33, 4, 1230 (2007) · Zbl 1138.93045 |
| [21] | Cao, J.; Wang, Z.; Sun, Y., Physica A, 385, 2, 718 (2007) |
| [22] | Sun, Y.; Cao, J.; Wang, Z., Neurocomputing, 70, 13-15, 2477 (2007) |
| [23] | Lu, J. G.; Xi, Y. G., Chaos Solitons Fractals, 17, 5, 825 (2003) · Zbl 1043.93518 |
| [24] | Yang, S. S.; Duan, C. K., Chaos Solitons Fractals, 9, 10, 1703 (1998) · Zbl 0946.34040 |
| [25] | Hu, A. H.; Xu, Z. Y.; Li, F., J. Syst. Simul., 18, 4, 981 (2006) |
| [26] | Xu, S.; Chen, T., IEEE Trans. Automat. Control, 47, 5, 2089 (2002) · Zbl 1364.93755 |
| [27] | Li, C.; Chen, L.; Aihara, K., BMC Syst. Biol., 1, 6 (2007) |
| [28] | Abarbanel, H. D.I.; Rulkov, N. F.; Sushchik, M. M., Phys. Rev. E, 53, 5, 4528 (1996) |
| [29] | Chua, L. O., J. Circuits Systems Comp., 4, 2, 117 (1994) |
| [30] | Lorenz, E. N., J. Atmos. Sci., 20, 3, 130 (1963) · Zbl 1417.37129 |
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