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Finite time synchronization of chaotic systems. (English) Zbl 1038.37504
Summary: Using finite time control techniques, continuous state feedback control laws are developed to solve the synchronization problem of two chaotic systems. We demonstrate that these two chaotic systems can be synchronized in finite time. Examples of Duffing systems and Lorenz systems are presented to verify our method.

MSC:
37D45Strange attractors, chaotic dynamics
93D15Stabilization of systems by feedback
37N35Dynamical systems in control
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References:
[1] Agiza, H. N.; Yassen, M. T.: Synchronization of Rössler and Chen chaotic dynamical systems using active control. Phys. lett. A 278, 191-197 (2001) · Zbl 0972.37019
[2] Bai, E. W.; Lonngen, K. E.: Synchronization of two Lorenz systems using active control. Chaos soliton. Fract. 8, 51-58 (1997)
[3] Bai, E. W.; Lonngen, K. E.: Synchronization and control of chaotic systems. Chaos soliton. Fract. 9, 1571-1575 (1999) · Zbl 0958.93513
[4] Bai, E. W.; Lonngen, K. E.: Sequential synchronization of two Lorenz systems using active control. Chaos soliton. Fract. 11, 1041-1044 (2000) · Zbl 0985.37106
[5] Bai, E. W.; Lonngen, K. E.; Sprott, J. C.: On the synchronization of electronic circuits that exhibit chaos. Chaos soliton. Fract. 13, 1515-1521 (2002) · Zbl 1005.34041
[6] Gong, X.; Lai, C. H.: On the synchronization of different chaotic oscillators. Chaos soliton. Fract. 11, 1231-1235 (2000) · Zbl 0955.34033
[7] Nijmerjer, H.: A dynamical control view on synchronization. Physica D 154, 219-228 (2001)
[8] Haimo, V. T.: Finite time controllers. SIAM J. Control optim. 24, 760-770 (1986) · Zbl 0603.93005
[9] Bhat S, Bernstein D. Finite-time stability of homogeneous systems, Proceedings of ACC, Albuquerque, NM; 1997. p. 2513--14