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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 647561, 13 pages
Impulsive Control for the Synchronization of Chaotic Systems with Time Delay
1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
Received 21 August 2012; Accepted 9 October 2012
Academic Editor: Jinde Cao
Copyright © 2012 Ming Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- H. N. Agiza and M. T. Yassen, “Synchronization of Rossler and Chen chaotic dynamical systems using active control,” Physics Letters A, vol. 278, no. 4, pp. 191–197, 2001.
- J. Q. Lu and J. D. Cao, “Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters,” Chaos, vol. 15, no. 4, Article ID 043901, 10 pages, 2005.
- J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, Article ID 013133, 6 pages, 2006.
- H. Zhang, X. K. Ma, and W. Z. Liu, “Synchronization of chaotic systems with parametric uncertainty using active sliding mode control,” Chaos, Solitons and Fractals, vol. 21, no. 5, pp. 1249–1257, 2004.
- Y. Ji, C. Y. Wen, and Z. G. Li, “Impulsive synchronization of chaotic systems via linear matrix inequalities,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 1, pp. 221–227, 2006.
- Y.-W. Wang, C. Wen, Y. C. Soh, and Z. H. Guan, “Partial state impulsive synchronization of a class of nonlinear systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 1, pp. 387–393, 2009.
- J. Q. Lu, D. W. C. Ho, and J. D. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010.
- Y. Liu, S. W. Zhao, and J. Q. Lu, “A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 393–398, 2011.
- B. Wu, Y. Liu, and J. Q. Lu, “Impulsive control of chaotic systems and its applications in synchronization,” Chinese Physics B, vol. 20, no. 5, Article ID 050508, 2011.
- B. Wu, Y. Liu, and J. Q. Lu, “New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 837–843, 2012.
- T. Yang and L. O. Chua, “Practical stability of impulsive synchronization between two nonautonomous chaotic systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 4, pp. 859–867, 2000.
- W. X. Xie, C. Y. Wen, and Z. G. Li, “Impulsive control for the stabilization and synchronization of Lorenz systems,” Physics Letters A, vol. 275, no. 1-2, pp. 67–72, 2000.
- Y. Li, “Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 713–719, 2010.
- L. Run-Zi, “Impulsive control and synchronization of a new chaotic system,” Physics Letters A, vol. 372, no. 5, pp. 648–653, 2008.
- X. Q. Wu, J. A. Lu, C. K. Tse, J. J. Wang, and J. Liu, “Impulsive control and synchronization of the Lorenz systems family,” Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 631–638, 2007.
- J. D. Cao, D. W. C. Ho, and Y. Q. Yang, “Projective synchronization of a class of delayed chaotic systems via impulsive control,” Physics Letters A, vol. 373, no. 35, pp. 3128–3133, 2009.
- C. Hu, H. J. Jiang, and Z. D. Teng, “Fuzzy impulsive control and synchronization of general chaotic system,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 463–485, 2010.
- M. Haeri and M. Dehghani, “Modified impulsive synchronization of hyperchaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 728–740, 2010.
- J. Chen, H. Liu, J. A. Lu, and Q. J. Zhang, “Projective and lag synchronization of a novel hyperchaotic system via impulsive control,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2033–2040, 2011.
- G. M. Liu and W. Ding, “Impulsive synchronization for a chaotic system with channel time-delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 958–965, 2011.
- X. Z. Liu, “Impulsive synchronization of chaotic systems subject to time delay,” Nonlinear Analysis, vol. 71, no. 12, pp. e1320–e1327, 2009.
- X. Z. Liu and Q. Wang, “Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 1, pp. 71–79, 2008.
- X. Z. Liu, X. S. Shen, Y. Zhang, and Q. Wang, “Stability criteria for impulsive systems with time delay and unstable system matrices,” IEEE Transactions on Circuits and Systems. I, vol. 54, no. 10, pp. 2288–2298, 2007.
- A. Khadra, X. Z. Liu, and X. S. Shen, “Analyzing the robustness of impulsive synchronization coupled by linear delayed impulses,” IEEE Transactions on Automatic Control, vol. 54, no. 4, pp. 923–928, 2009.
- C. Li, X. Liao, and X. Zhang, “Impulsive synchronization of chaotic systems,” Chaos, vol. 15, no. 2, Article ID 023104, 5 pages, 2005.
- J. Zhou and Q. J. Wu, “Exponential stability of impulsive delayed linear differential equations,” IEEE Transactions on Circuits and Systems II, vol. 56, no. 9, pp. 744–748, 2009.
- Q. Wang and X. Z. Liu, “Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method,” Applied Mathematics Letters, vol. 20, no. 8, pp. 839–845, 2007.