Advertisement

Nonlinear Dynamics

, Volume 94, Issue 2, pp 991–1002 | Cite as

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

  • Wookyong Kwon
  • Baeyoung Koo
  • S. M. Lee
Original Paper

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.

Keywords

Proportional-derivative event-triggered control Integrated event-triggering inequality Synchronization of chaotic system 

Notes

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).

References

  1. 1.
    Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–825 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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)MathSciNetCrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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. 12.
    Liu, Y., Lee, S.M.: Synchronization of chaotic Lure systems using sampled-data PD control. Nonlinear Dyn. 85(2), 981–992 (2016)CrossRefzbMATHGoogle Scholar
  13. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 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)CrossRefzbMATHGoogle Scholar
  15. 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)CrossRefzbMATHGoogle Scholar
  16. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 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)Google Scholar
  20. 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)MathSciNetCrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 22.
    Tipsuwan, Y., Chow, M.Y.: Control methodologies in networked control systems. Control Eng. Pract. 11(10), 1099–1111 (2003)CrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 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)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Elia, N., Mitter, S.K.: Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Yue, D., Han, Q.L., Lam, J.: Network-based robust H\(\infty \) control of systems with uncertainty. Automatica 41(6), 999–1007 (2005)MathSciNetCrossRefGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. 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)MathSciNetCrossRefGoogle Scholar
  30. 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)MathSciNetCrossRefGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Seuret, A., Briat, C.: Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals. Automatica 55, 274–278 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Zeng, H.B., Teo, K., He, Y.: A new looped-functional for stability analysis of sampled-data systems. Automatica 82, 328–331 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Graduate Institute of Ferrous TechnologyPohang University of Science and TechnologyPohangRepublic of Korea
  2. 2.School of Electronics EngineeringKyungpook National UniversityDaeguRepublic of Korea

Personalised recommendations