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


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.


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



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).


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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

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