Leader-following Consensus of Nonlinear Multi-agent Systems via Reliable Control with Time-varying Communication Delay

  • K. Subramanian
  • P. Muthukumar
  • Young Hoon JooEmail author
Regular Papers Control Theory and Applications


This paper investigates the consensus problem of continuous-time leader-following nonlinear multi-agent systems with time-varying communication delay via reliable control. The parameter uncertainty is assumed to be bounded in given compact sets. With certain assumptions on the dynamic nonlinearity and underlying topology, the sufficient conditions are derived in terms of linear matrix inequality (LMI) by using a suitable Lyapunov- Krasovskii functional (LKF). It is ensure that the leader-following consensus can be achieved under the proposed reliable control scheme. Finally, numerical simulation results are presented to demonstrate the theoretical results.


Communication delay leader-following consensus linear matrix inequality multi-agent systems reliable control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Z. Li and Z. Duan, Cooperative Control of Multi–agent Systems: A Consensus Region Approach, CRC Press, New York, 2014.CrossRefGoogle Scholar
  2. [2]
    Z. Peng, G. Wen, S. Yang, and A. Rahmani, “Distributed consensus–based formation control for nonholonomic wheeled mobile robots using adaptive neural network,” Nonlinear Dynamimcs, vol. 86, no. 1, pp. 605–622, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S. Yang, Y. Cao, Z. Peng, G. Wen, and K. Guo, “Distributed formation control of nonholonomic autonomous vehicle via RBF neural network,” Mechanical Systems and Signal Processing, vol. 87, pp. 81–95, 2017.CrossRefGoogle Scholar
  4. [4]
    H. Zhang, D. Yue, X. Yin, S. Hu, and C. X. Dou, “Finite–time distributed event–triggered consensus control for multi–agent systems,” Information Sciences, vol. 339, pp. 132–142, 2016.CrossRefzbMATHGoogle Scholar
  5. [5]
    D. Zhang, Z. Xu, Q. G. Wang, and Y. B. Zhao, “Leaderfollower H¥ consensus of linear multi–agent systems with aperiodic sampling and switching connected topologies,” ISA Transactions, vol. 68, pp. 150–159, 2017.CrossRefGoogle Scholar
  6. [6]
    W. He, B. Zhang, Q. L. Han, F. Qian, J. Kurths, and J. Cao, “Leader–following consensus of nonlinear multiagent systems with stochastic sampling,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 327–338, 2017.Google Scholar
  7. [7]
    D. Li, J. Ma, H. Zhu, and M. Sun, “The consensus of multiagent systems with uncertainties and randomly occurring nonlinearities via impulsive control,” International Journal of Control, Automation and Systems, vol. 14, no. 4, pp. 1005–1011, 2016.CrossRefGoogle Scholar
  8. [8]
    R. Rakkiyappan, B. Kaviarasan, and J. Cao, “Leaderfollowing consensus of multi–agent systems via sampleddata control with randomly missing data,” Neurocomputing, vol. 161, pp. 132–147, 2015.CrossRefGoogle Scholar
  9. [9]
    M. Lu and L. Liu, “Consensus of linear multi–agent systems subject to communication delays and switching networks,” International Journal of Robust and Nonlinear Control, vol. 27, no. 9, pp. 1379–1396, 2017.MathSciNetzbMATHGoogle Scholar
  10. [10]
    Y. Xu, S. Peng, and A. Guo, “Leader–following consensus of nonlinear delayed multi–agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input,” International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 566–576, 2018.CrossRefGoogle Scholar
  11. [11]
    L. Li, D. W. Ho, and J. Lu, “Event–based network consensus with communication delays,” Nonlinear Dynamics, vol. 87, no. 3, pp. 1847–1858, 2017.CrossRefzbMATHGoogle Scholar
  12. [12]
    J. Qin, H. Gao, and W. X. Zheng, “Second–order consensus for multi–agent systems with switching topology and communication delay,” Systems & Control Letters, vol. 60, no. 6, pp. 390–397, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Q. Zhang, Y. Niu, L.Wang, L. Shen, and H. Zhu, “Average consensus seeking of high–order continuous–time multiagent systems with multiple time–varying communication delays,” International Journal of Control, Automation and Systems, vol. 9, no. 6, pp. 1209–1218, 2011.CrossRefGoogle Scholar
  14. [14]
    H. S. Kim, J. B. Park, and Y. H. Joo, “Less conservative robust stabilization conditions for the uncertain polynomial fuzzy system under perfect and imperfect premise matching,” International Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1588–1598, 2016.CrossRefGoogle Scholar
  15. [15]
    D. H. Lee, M. H. Tak, and Y. H. Joo, “A Lyapunov functional approach to robust stability analysis of continuoustime uncertain linear systems in polytopic domains,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 460–469, 2013.CrossRefGoogle Scholar
  16. [16]
    R. Saravanakumar, M. S. Ali, H. Huang, J. Cao, and Y. H. Joo, “Robust H¥ state–feedback control for nonlinear uncertain systems with mixed time–varying delays,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 225–233, 2018.CrossRefGoogle Scholar
  17. [17]
    C. Li, X. Liao, and R. Zhang, “Global robust asymptotical stability of multi–delayed interval neural networks: an LMI approach,” Physics Letters A, vol. 328, no. 6, pp. 452–462, 2004.CrossRefzbMATHGoogle Scholar
  18. [18]
    X. Xu, Z. Li, and L. Gao, “Distributed adaptive tracking control for multi–agent systems with uncertain dynamics,” Nonlinear Dynamics, vol. 90, no. 4, pp. 2729–2744, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Z. Li, Y. Zhao, and Z. Duan, “Distributed robust consensus of a class of Lipschitz nonlinear multi–agent systems with matching uncertainties,” Asian Journal of Control, vol. 1. no. 1, pp. 3–13, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Y. Wang, Y. Song, M. Krstic, and C. Wen, “Fault–tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single–way directed communication interactions and actuation failures,” Automatica, vol. 63, pp. 374–383, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    C. H. Xie and G. H. Yang, “Cooperative guaranteed cost fault–tolerant control for multi–agent systems with timevarying actuator faults,” Neurocomputing, vol. 214, pp. 382–390, 2016.CrossRefGoogle Scholar
  22. [22]
    G. Zhang, J. Qin, W. X. Zheng, and Y. Kang, “Faulttolerant coordination control for second–order multi–agent systems with partial actuator effectiveness,” Information Sciences, vol. 423, pp. 115–127, 2018.MathSciNetCrossRefGoogle Scholar
  23. [23]
    O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “On stability analysis for neural networks with interval time–varying delays via some new augmented Lyapunov–Krasovskii functional,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3184–3201, 2014.MathSciNetCrossRefGoogle Scholar
  24. [24]
    M. V. Thuan and V. N. Phat, “Optimal guaranteed cost control of linear systems with mixed interval time–varying delayed state and control,” Journal of Optimization Theory and Applications, vol. 152, no. 2, pp. 394–412, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    H. Wu, X. Liao, W. Feng, S. Guo, and W. Zhang, “Robust stability analysis of uncertain systems with two additive time–varying delay components,” Applied Mathematical Modelling, vol. 33, no. 12, pp. 4345–4353, 2009.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • K. Subramanian
    • 1
  • P. Muthukumar
    • 1
  • Young Hoon Joo
    • 2
    Email author
  1. 1.Department of MathematicsThe Gandhigram Rural Institute (Deemed to be University)GandhigramIndia
  2. 2.School of IT Information and Control EngineeringKunsan National UniversityKunsanKorea

Personalised recommendations