Event-Triggered Based Synchronization of Linear Singularly Perturbed Systems

  • Nakul Kotibhaskar
  • Kritika Bansal
  • Pankaj Mukhija
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 989)


This paper addresses the synchronization problem in a complex dynamical network where each node is considered a linear singularly perturbed system. A network is considered where the slow dynamics of one node may be coupled with fast dynamics of the other nodes and vice versa. Two-time scale separation of the overall network is shown and feedback control is designed using classical singular perturbation theory. Considering the limited network resources, an event-triggering mechanism is designed separately for the slow and fast states of the overall network, such that synchronization is achieved without Zeno behaviour.


Synchronization Singular perturbation Event-triggered Complex dynamical network 


  1. 1.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440 EP (1998)CrossRefGoogle Scholar
  2. 2.
    Kokotovic, P., Khalil, H.K., Oreilly., J.: Singular perturbation methods in control: analysis and design. SIAM (1999)Google Scholar
  3. 3.
    Wang, X.F., Chen, G.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos (2002)Google Scholar
  4. 4.
    Tu, L., Lu, J.A.: Delay-dependent synchronization in general complex delayed dynamical networks. Comput. Math. Appl. 57(1), 28–36 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Li, N., Zhang, Y., Hu, J., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74(5), 805–811 (2011)CrossRefGoogle Scholar
  6. 6.
    Xu, M., Wang, J.L., Huang, Y.L., Wei, P.C., Wang, S.X.: Pinning synchronization of complex dynamical networks with and without time-varying delay. Neurocomputing 266, 263–273 (2017)CrossRefGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cai, C., Wang, Z., Xu, J., Alsaedi, A.: Decomposition approach to exponential synchronisation for a class of non-linear singularly perturbed complex networks. IET Control. Theory Appl. 8(16), 1639–1647 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cai, C., Wang, Z., Xu, J., Liu, X., Alsaadi, F.E.: An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks. IEEE Trans. Cybern. 45(8), 1597–1609 (2015)CrossRefGoogle Scholar
  10. 10.
    Cai, C., Xu, J., Liu, Y., Zou, Y.: Synchronization for linear singularly perturbed complex networks with coupling delays. Int. J. Gen. Syst. 44(2), 240–253 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Peng, C., Li, F.: A survey on recent advances in event-triggered communication and control. Inf. Sci. 457–458, 113–125 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Li, Q., Shen, B., Liang, J., Shu, H.: Event-triggered synchronization control for complex networks with uncertain inner coupling. Int. J. Gen. Syst. 44(2), 212–225 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Liu, T., Cao, M., Persis, C.D., Hendrickx, J.M.: Distributed event-triggered control for synchronization of dynamical networks with estimators*. IFAC Proc. Vol. 46(27), 116–121 (2013). (4th IFAC Workshop on Distributed Estimation and Control in Networked Systems)CrossRefGoogle Scholar
  14. 14.
    Sivaranjani, K., Rakkiyappan, R., Cao, J., Alsaedi, A.: Synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control. Appl. Math. Comput. 311, 283–299 (2017)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Schäcke, K.: On the kronecker product kathrin schäcke (2013)Google Scholar
  16. 16.
    Bhandari, M., Fulwani, D.M., Gupta, R.: Event-triggered composite control of a two time scale system. IEEE Trans. Circuits Syst. II: Express Briefs 65(4), 471–475 (2018)CrossRefGoogle Scholar
  17. 17.
    Abdelrahim, M., Postoyan, R., Daafouz, J.: Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics. In: 9th IFAC Symposium on Nonlinear Control Systems. NOLCOS 2013, pp. 347–352. Toulouse, France (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Nakul Kotibhaskar
    • 1
  • Kritika Bansal
    • 2
  • Pankaj Mukhija
    • 2
  1. 1.New DelhiIndia
  2. 2.National Institute of Technology DelhiNew DelhiIndia

Personalised recommendations