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Asymptotical Synchronization of Chaotic Lur’e Systems Under Time-Varying Sampling

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Abstract

This paper investigates the problem of sampled-data synchronization of chaotic Lur’e systems with time-varying sampling. A novel Lyapunov functional, which is continuous in time and makes full use of the available information about the sampling pattern, is constructed to synchronize the chaotic Lur’e systems. By using a free-weighting matrix approach and solving a set of linear matrix inequalities (LMIs), a sampled-data controller is obtained. The effectiveness and the validity of the proposed theoretical result are illustrated by two numerical examples.

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References

  1. J.G. Barajas-Ramirez, G. Chen, L.S. Shieh, Hybrid chaos synchronization. Int. J. Bifurc. Chaos Appl. Sci. Eng. 13(5), 1197–1216 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. J.G. Barajas-Ramirez, G. Chen, L.S. Shieh, Fuzzy chaos synchronization via sampled driving signals. Int. J. Bifurc. Chaos Appl. Sci. Eng. 14(8), 2721–2723 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Boutayeb, M. Darouach, H. Rafaralahy, Generalized state-space observers for chaotic synchronization and secure communication. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49(3), 345–349 (2002)

    Article  MathSciNet  Google Scholar 

  4. T.L. Carroll, L.M. Pecora, Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. 38(4), 453–456 (1991)

    Article  Google Scholar 

  5. A.L. Fradkov, B. Andrievsky, R.J. Evans, Synchronization of passifiable Lurie systems via limited-capacity communication channel. IEEE Trans. Circuits Syst. I, Regul. Pap. 56(2), 430–439 (2009)

    Article  MathSciNet  Google Scholar 

  6. E. Fridman, A refined input delay approach to sampled-data control. Automatica 46(2), 421–427 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Q.L. Han, On designing time-varying delay feedback controller for master–slave synchronization of Lur’e systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(7), 1573–1583 (2007)

    Article  MathSciNet  Google Scholar 

  8. Y. He, Q. Wang, L. Xie, C. Lin, Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52(2), 293–299 (2007)

    Article  MathSciNet  Google Scholar 

  9. Y. He, G.L. Wen, Q.G. Wang, Delay-dependent synchronization criterion for Lur’e systems with delay feedback control. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16(10), 3087–3091 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. He, M. Wu, J.H. She, G.P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51(1), 57–65 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Y. He, M. Wu, J.H. She, G.P. Liu, Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans. Autom. Control 49(5), 828–832 (2004)

    Article  MathSciNet  Google Scholar 

  12. G. Hu, Z. Feng, R. Meng, Chosen ciphertext attack on chaos communication based on chaotic synchronization. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50(2), 257–279 (2003)

    Google Scholar 

  13. Z. Hu, H. Zhu, J. Zhao, Further results on H ∞ filtering for a class of discrete-time singular systems with interval time-varying delay. Circuits Syst. Signal Process. (2013). doi:10.1007/s00034-012-9491-1

    MathSciNet  Google Scholar 

  14. J. Huang, Y. Yang, Z. Han, J. Zhang, Robust absolute stability criterion for uncertain Lur’e differential inclusion systems with time delay. Circuits Syst. Signal Process. 31(6), 2001–2017 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. J.H. Kim, C.H. Hyun, E. Kim, Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15(3), 359–369 (2007)

    Article  Google Scholar 

  16. A.P. Kurian, S. Puthusserypady, Performance analysis of nonlinear-predictive-filter-based chaotic synchronization. IEEE Trans. Circuits Syst. II, Express Briefs 53(7), 886–890 (2006)

    Article  Google Scholar 

  17. J. Lu, D.J. Hill, Global asymptotical synchronization of chaotic Lur’e systems using sampled data: a linear matrix inequality approach. IEEE Trans. Circuits Syst. II, Express Briefs 55(6), 586–590 (2008)

    Article  Google Scholar 

  18. T. Papamarkou, A.J. Lawrance, Paired Bernoulli circular spreading: attaining the BER lower bound in a CSK setting. Circuits Syst. Signal Process. 32(1), 143–166 (2013)

    Article  MathSciNet  Google Scholar 

  19. J.A.K. Suykens, T. Yang, L.O. Chua, Impulsive synchronization of chaotic Lur’e systems by measurement feedback. Int. J. Bifurc. Chaos Appl. Sci. Eng. 8(6), 1371–1381 (1998)

    Article  MATH  Google Scholar 

  20. Y. Wang, X. Zhang, Y. Hu, Robust H ∞ control for a class of uncertain neutral stochastic systems with mixed delays: a ccl approach. Circuits Syst. Signal Process. 32(2), 631–646 (2013)

    Article  MathSciNet  Google Scholar 

  21. Z. Wu, P. Shi, H. Su, J. Chu, Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans. Neural Netw. Learn. Syst. 23(9), 1368–1376 (2012)

    Article  Google Scholar 

  22. M.E. Yalcin, J.A.K. Suykens, J.P.L. Vandewalle, Master–slave synchronization of Lur’e systems with time-delay. Int. J. Bifurc. Chaos Appl. Sci. Eng. 11(6), 1707–1722 (2001)

    Article  Google Scholar 

  23. M.E. Yalcin, J.A.K. Suykens, J.P.L. Vandewalle, Cellular Neural Networks, Multi-Scroll Chaos and Synchronization (World Scientific, Singapore, 2005)

    MATH  Google Scholar 

  24. C. Zhang, Y. He, M. Wu, Improved global asymptotical synchronization of chaotic Lur’e systems with sampled-data control. IEEE Trans. Circuits Syst. II, Express Briefs 56(4), 320–324 (2009)

    Article  Google Scholar 

  25. X. Zhu, Y. Wang, H. Yang, New globally asymptotical synchronization of chaotic Lur’e systems using sampled data, in Processing of the 28th American Control Conference, (2010), pp. 1817–1822

    Google Scholar 

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Acknowledgements

This work is supported by The National Natural Science Foundation of P.R. China (61304072), National Natural Science Foundation of P.R. China (61203025) and National Basic Research Program of China (2013CB035406)

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Authors and Affiliations

  1. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou Zhejiang, 310027, P.R. China

    Yuan-Qing Wu, Hongye Su & Zheng-Guang Wu

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  1. Yuan-Qing Wu
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  2. Hongye Su
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Correspondence to Hongye Su.

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Wu, YQ., Su, H. & Wu, ZG. Asymptotical Synchronization of Chaotic Lur’e Systems Under Time-Varying Sampling. Circuits Syst Signal Process 33, 699–712 (2014). https://doi.org/10.1007/s00034-013-9665-5

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  • DOI: https://doi.org/10.1007/s00034-013-9665-5

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