Skip to main content

Advertisement

Springer Nature Link
Log in

Further Criteria on Master–Slave Synchronization in Chaotic Lur’e Systems Using Delay Feedback Control

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper is concerned with designing delay feedback controllers of master–slave synchronization for Lur’e systems. Through dividing the delay interval into two parts and choosing two augmented Lyapunov–Krasovskii functionals, some delay-dependent synchronization criteria are formulated in terms of linear matrix inequalities (LMIs), in which the conservatism can be effectively reduced based on adjusting some useful parameters. The proposed conditions can be easily checked, and the controller gains can be achieved by solving the derived LMIs. Finally, two numerical examples are given to illustrate the presented results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. D. Banjerdpongchai, H. Kimura, Robust analysis of discrete-time Lur’e systems with slope restrictions using convex optimization. Asian J. Control 4(2), 119–126 (2002)

    Article  Google Scholar 

  2. T.S. Banerjee, P. Balasubramaniam, Synchronization of chaotic systems under sampled-data control. Nonlinear Dyn. 70(3), 1977–1987 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Balasubramaniam, R. Chandran, S. Theesar, Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn. Neurodyn. 5(4), 361–371 (2011)

    Article  Google Scholar 

  4. P. Balasubramaniam, Vembarasan, synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback. Nonlinear Dyn. 70(1), 677–691 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Carroll, L. Pecora, Synchronization chaotic circuits. IEEE Trans. Circ. Syst. 38(4), 453–456 (1991)

    Article  Google Scholar 

  6. Y. Chun, S.M. Zhong, W.F. Chen, Design PD controller for master-slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1632–1639 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. W.H. Chen, Z.P. Wang, X.M. Lu, On sampled-data control for master–slave synchronization of chaotic Lur’e systems. IEEE Trans. Circ. Syst. 59(8), 515–519 (2012)

    Article  Google Scholar 

  8. A.L. Fradkov, B. Andrievsky, R.J. Evans, Synchronization of nonlinear systems via under information constraints. Chaos 18(1), 037109 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Ge, C.C. Hua, X.P. Guan, Master–slave synchronization criteria of Lur’e systems with time-delay feedback control. Appl. Math. Comput. 244(1), 895–902 (2014)

    MathSciNet  MATH  Google Scholar 

  10. H. Huang, J.D. Cao, Master–slave synchronization of Lur’e systems based on time-varying delay feedback control. Int. J. Bifurc. Chaos 17(11), 4159–4166 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Y. He, G.L. Wen, Q.G. Wang, Delay-dependent synchronization criterion for Lur’e systems with delay feedback control. Int. J. Bifurc. Chaos 16(2), 3087–3091 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. W.L. He, F. Qian, Q.L. Han, Synchronization error estimation and controller design for delayed Lur’e systems with parameter mismatches. IEEE Trans. Neural Netw. Learn. Syst. 33(1), 1551–1563 (2012)

    Google Scholar 

  14. X.F. Ji, W.N. Zhou, H.Y. Su, On Designing time-delay feedback controller for master–slave synchronization of Lur’e systems. Asian J. Control 16(1), 308–312 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. X.F. Ji, C. Zu, H.Y. Su, Delay-dependent synchronisation for singular Lur’e systems using time delay feedback control. Int. J. Model. Identif. Control 19(2), 125–133 (2013)

    Article  Google Scholar 

  16. H.R. Karimi, A sliding mode approach to H-infinity synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. J. Frankl. Instit. 349(4), 1480–1496 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. H.H. Kuo, T.L. Liao, J.J. Yan, Design and synchronization of master–slave electronic horizontal platform system. Disc. Dyn. Nat. Soc. 1–11, 948126 (2012)

    MathSciNet  MATH  Google Scholar 

  18. H.R. Karimi, M. Zapateiro, N.S. Luo, Adaptive synchronization of master–slave systems with mixed neutral and discrete time-delays and nonlinear perturbations. Asian J. Control 14(1), 251–257 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. S.M. Lee, Ju H. Park, O.M. Kwon, Improved asymptotic stability analysis for Lur’e systems with sector and slope restricted nonlinearities. Phys. Lett. A 362(5–6), 348–351 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. S.M. Lee, S.J. Choi, D.H. Ji, J.H. Park, S.C. Won, Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control. Nonlinear Dyn. 59(11), 277–288 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. T. Li, J.J. Yu, Z. Wang, Delay-range-dependent synchronization criterion for Lur’e systems with delay feedback control. Commun. Nonlinear Sci. Numer. Simul. 14(2), 1796–1803 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. T. Li, A.G. Song, S.M. Fei, Master–slave synchronization for delayed Lur’e systems using time-delay feedback control. Asian J. Control 13(6), 879–892 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Liu, J. Zhang, Note on stability of discrete-time time-varying delay systems. IET Control Theor. Appl. 6(2), 335–339 (2012)

    Article  MathSciNet  Google Scholar 

  24. H. Mkaouar, O. Boubaker, Chaos synchronization for master slave piecewise linear systems: application to Chua’s circuit. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1292–1302 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. V.F. Montagner, R.C. Oliveira, T.R. Calliero, Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur’e functions. Nonlinear Anal. Theory Methods Appl 70(5), 1803–1812 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. L. Pecora, T. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Rakkiyappan, R. Sivasamy, S. Lakshmanan, Exponential synchronization of chaotic Lur’e systems with time-varying delay via sampled-data control. Chin. Phys. B 23(6), 060504 (2014)

    Article  Google Scholar 

  28. F.O. Souza, R.M. Palhares, E.M.A.M. Mendes, Further results on master–slave synchronization of general Lur’e systems with time-varying delay. Int. J. Bifurc. Chaos 18(1), 187–202 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Theesar, R. Chandran, P. Balasubramaniam, Delay-dependent exponential synchronization criteria for chaotic neural networks with time-varying delays. Brazil. J. Phys. 42(3–4), 207–218 (2012)

    Article  Google Scholar 

  30. S.J. Theesar, P. Balasubramaniam, Secure communication via synchronization of Lur’e systems using sampled-data controller. Circuits Syst. Signal Proc. 33(1), 37–52 (2014)

    Article  MathSciNet  Google Scholar 

  31. T.B. Wang, W.N. Zhou, S.W. Zhao, Robust master-slave synchronization for general uncertain delayed dynamical model based on adaptive control scheme. ISA Trans. 53(2), 335–340 (2014)

    Article  MathSciNet  Google Scholar 

  32. Z.G. Wu, P. Shi, H.Y. Su, 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 

  33. T.B. Wang, S.W. Zhao, W.N. Zhou, Finite-time master–slave synchronization and parameter identification for uncertain Lurie systems. ISA Trans. 53(4), 1184–1190 (2014)

    Article  MathSciNet  Google Scholar 

  34. Z.G. Wu, P. Shi, H.Y. Su, Sampled-data synchronization of chaotic Lur’e systems with time delays. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 410–421 (2013)

    Article  Google Scholar 

  35. W.Q. Wang, S.K. Nhguang, S.M. Zhong, F. Liu, Novel delay-dependent stability criterion for time-varying delay systems with parameter uncertainties and nonlinear perturbations. Inform. Sci. 281(10), 321–333 (2014)

    Article  MathSciNet  Google Scholar 

  36. J. Xiang, Y.J. Li, W. Wei, An improved condition for master–slave synchronization of Lur’e systems with time delay. Phys. Lett. A. 362(2–3), 154–158 (2007)

    Article  Google Scholar 

  37. X.Q. Xiao, L. Zhou, Z.J. Zhang, Synchronization of chaotic Lur’e systems with quantized sampled-data controller. Commun. Nonlinear Sci. Numer. Simul. 19(6), 2039–2047 (2014)

    Article  MathSciNet  Google Scholar 

  38. J.Q. Yang, Y.T. Chen, F.L. Zhu, Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication. Appl. Math. Comput. 229(25), 227–238 (2014)

    Google Scholar 

  39. J.Q. Yang, F.L. Zhu, Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers. Communic. Nonlinear Sci. Numer. Simul. 18(4), 926–937 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  40. D.S. Yang, Z.W. Liu, Y. Zhao, Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies. Chin. Phys. B 21(4), 040503 (2012)

    Article  Google Scholar 

  41. M.E. Yalein, J.A.K. Suykens, J. Vandewalle, Master–slave synchronization of Lur’e systems with time-delay. Int. J. Bifurc. Chaos. 11(6), 1707–1722 (2001)

    Article  Google Scholar 

  42. J. Zhong, L.Q. Lu, T.W. Huang, Synchronization of master-slave Boolean networks with impulsive effects: necessary and sufficient criteria. Neurocomputing 143(5), 269–274 (2014)

    Article  Google Scholar 

  43. C.K. Zhang, L. Jiang, Y. He, Q.H. Wu, Asymptotical synchronization for chaotic Lur’e systems using sampled-data control. Communic. Nonlinear Sci. Numer. Simul. 18(10), 2743–2751 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  44. X.M. Zhang, G.P. Lu, Y.F. Zhang, Synchronization for time-delay Lur’e systems with sector and slope restricted nonlinearities under communication constraints. Circuits Syst. Signal Proc. 30(6), 1573–1593 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 61374116, 61473079, 61473047), Jiangsu Natural Science Foundation (Nos. SBK201240801, BKs2012384) and the Open Founds of Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education (No. MCCSE2013A04).

Author information

Authors and Affiliations

  1. School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Tao Li & Shaojie Zhang

  2. Key Laboratory of Measurement and Control of CSE (School of Automation, Southeast University), Ministry of Education, Nanjing, 210096, People’s Republic of China

    Tao Li, Guobao Zhang & Shumin Fei

Authors
  1. Tao Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Guobao Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Shumin Fei
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Shaojie Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Tao Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, T., Zhang, G., Fei, S. et al. Further Criteria on Master–Slave Synchronization in Chaotic Lur’e Systems Using Delay Feedback Control. Circuits Syst Signal Process 35, 2992–3014 (2016). https://doi.org/10.1007/s00034-015-0167-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0167-5

Keywords