Skip to main content

Advertisement

SpringerLink
Log in

Integral-based event-triggered synchronization criteria for chaotic Lur’e systems with networked PD control

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Integral-based event-triggered synchronization criteria are firstly presented for networked chaotic systems with proportional-derivative (PD) control. The event-triggered scheme effectively utilizes network resources; however, the PD-type control subject to the conventional triggering inequality may cause excessive triggering and have difficulty in obtaining a feasible solution. To solve these problems, the integrated event-triggering inequality is employed and the modified integral inequality with free-weighting matrix is proposed to fill the empty diagonal terms, which overcomes the difficulties of the integration of delayed signal vectors upon integral event-triggering condition. Based on Lyapunov stability, the synchronization criteria are derived as linear matrix inequalities. Finally, the effectiveness of the integral-based event-triggered synchronization method is demonstrated by numerical examples.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–825 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ge, C., Li, Z., Huang, X., Shi, C.: New globally asymptotical synchronization of chaotic systems under sampled-data controller. Nonlinear Dyn. 78(4), 2409–2419 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Xiao, X., Zhou, L., Zhang, Z.: Synchronization of chaotic Lure systems with quantized sampled-data controller. Commun. Nonlinear Sci. Numer. Simul. 19(6), 2039–2047 (2014)

    Article  MathSciNet  Google Scholar 

  4. Xiao, S.P., Liu, X., Zhang, C.F., Zeng, H.B.: Further results on absolute stability of Lur e systems with a time-varying delay. Neurocomputing 207, 823–827 (2016)

    Article  Google Scholar 

  5. Lu, J.G., Hill, D.J.: 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 

  6. Zhang, C.K., He, Y., Wu, M.: 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 

  7. Martnez-Guerra, R., Garca, J.J.M., Prieto, S.M.D.: Secure communications via synchronization of Liouvillian chaotic systems. J. Franklin Inst. 353(17), 4384–4399 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Sharma, V., Sharma, B.B., Nath, R.: Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty. Chaos Solitons Fractals 96, 51–58 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rakkiyappan, R., Sivaranjani, K.: Sampled-data synchronization and state estimation for nonlinear singularly perturbed complex networks with time-delays. Nonlinear Dyn. 84(3), 1623–1636 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shang-Guan, X.C., He, Y., Lin, W.J., Wu, M.: Improved synchronization of chaotic Lur’e systems with time delay using sampled-data control. J. Franklin Inst. 354(3), 1618–1636 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, Y., Lee, S.M.: Stability and stabilization of Takagi-Sugeno fuzzy systems via sampled-data and state quantized controller. IEEE Trans. Fuzzy Syst. 24(3), 635–644 (2016)

    Google Scholar 

  12. Liu, Y., Lee, S.M.: Synchronization of chaotic Lure systems using sampled-data PD control. Nonlinear Dyn. 85(2), 981–992 (2016)

    Article  MATH  Google Scholar 

  13. Liu, S., Zhou, L.: Network synchronization and application of chaotic Lur’e systems based on event-triggered mechanism. Nonlinear Dyn. 83(4), 2497–2507 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, S., Zhou, L.: Network synchronization and application of chaotic Lure systems based on event-triggered mechanism. Nonlinear Dyn. 83(4), 2497–2507 (2016)

    Article  MATH  Google Scholar 

  15. Zeng, D., Wu, K., Liu, Y., Zhang, R., Zhong, S.: Event-triggered sampling control for exponential synchronization of chaotic Lur’e systems with time-varying communication delays. Nonlinear Dyn. 91(2), 905–921 (2018)

    Article  MATH  Google Scholar 

  16. Yue, D., Tian, E., Han, Q.L.: A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58(2), 475–481 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shen, H., Su, L., Wu, Z.G., Park, J.H.: Reliable dissipative control for Markov jump systems using an event-triggered sampling information scheme. Nonlinear Anal. Hybrid Syst. 25, 41–59 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mousavi, S. H., Ghodrat, M., Marquez, H. J.: A novel integral-based event triggering control for linear time-invariant systems. In: 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE (2014)

  20. Mousavi, S.H., Ghodrat, M., Marquez, H.J.: Integral-based event-triggered control scheme for a general class of non-linear systems. IET Control Theory Appl. 9(13), 1982–1988 (2015)

    Article  MathSciNet  Google Scholar 

  21. Lian, F.L., Moyne, J., Tilbury, D.: Network design consideration for distributed control systems. IEEE Trans. Control Syst. Technol. 10(2), 297–307 (2002)

    Article  Google Scholar 

  22. Tipsuwan, Y., Chow, M.Y.: Control methodologies in networked control systems. Control Eng. Pract. 11(10), 1099–1111 (2003)

    Article  Google Scholar 

  23. Meng, Z., Ren, W., Cao, Y.: Leaderless and leader-following consensus with communication and input delays under a directed network topology. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41(1), 75–88 (2011)

    Article  Google Scholar 

  24. Koo, B., Kwon, W., Lee, S.: Integral-based event-triggered PD control for systems with network-induced delay using a quadratic generalised free-weighting matrix inequality. IET Control Theory Appl. 11(18), 3261–3268 (2017)

    Article  MathSciNet  Google Scholar 

  25. Elia, N., Mitter, S.K.: Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  26. Yue, D., Han, Q.L., Lam, J.: Network-based robust H\(\infty \) control of systems with uncertainty. Automatica 41(6), 999–1007 (2005)

    Article  MathSciNet  Google Scholar 

  27. Lin, W.J., He, Y., Zhang, C.K., Wu, M., Ji, M.D.: Stability analysis of recurrent neural networks with interval time-varying delay via free-matrix-based integral inequality. Neurocomputing 205, 490–497 (2016)

    Article  Google Scholar 

  28. Lee, T.H., Xia, J., Park, J.H.: Networked control systems with asynchronous sampling and quantizations in both transmission and receiving channels. Neurocomputing 236(1), 25–38 (2017)

    Article  Google Scholar 

  29. Selvi, S., Sakthivel, R., Mathiyalagan, K.: Robust sampled-data control of uncertain switched neutral systems with probabilistic input delay. Complexity 21(5), 308–318 (2016)

    Article  MathSciNet  Google Scholar 

  30. Zhang, X.M., Han, Q.L., Zhang, B.L.: An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems. IEEE Trans. Industr. Inf. 13(1), 4–16 (2017)

    Article  MathSciNet  Google Scholar 

  31. Zhang, X.M., Han, Q.L.: A decentralized event-triggered dissipative control scheme for systems with multiple sensors to sample the system outputs. IEEE Trans. Cybern. 46(12), 2745–2757 (2016)

    Article  Google Scholar 

  32. Briat, C., Seuret, A.: A looped-functional approach for robust stability analysis of linear impulsive systems. Syst. Control Lett. 61(10), 980–988 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  33. Seuret, A., Briat, C.: Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals. Automatica 55, 274–278 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  34. Zeng, H.B., Teo, K., He, Y.: A new looped-functional for stability analysis of sampled-data systems. Automatica 82, 328–331 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2016R1D1A1B03930623).

Author information

Authors and Affiliations

  1. Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang, Gyungbuk, Republic of Korea

    Wookyong Kwon & Baeyoung Koo

  2. School of Electronics Engineering, Kyungpook National University, Daegu, Republic of Korea

    S. M. Lee

Authors
  1. Wookyong Kwon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baeyoung Koo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. M. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. M. Lee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kwon, W., Koo, B. & Lee, S.M. Integral-based event-triggered synchronization criteria for chaotic Lur’e systems with networked PD control. Nonlinear Dyn 94, 991–1002 (2018). https://doi.org/10.1007/s11071-018-4405-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4405-9

Keywords

Search

Navigation