Leaderless Consensus of Non-linear Mixed delay Multi-agent Systems with Random Packet Losses via Sampled-data Control


This paper inspects the consensus problem of nonlinear mixed delay multi-agent systems with random packet losses through the sampled-data control using the undirected graph without any specified leader for the other following agents. The probabilistic time varying delay is taken in the control input delay that Bernoulli distributed white sequence is engaged to formulate the random packet losses between the agents. The consensus problem can be changed over into a stabilization problem by using the Laplacian matrix which can be obtained by undirected graph. By framing a Lyapunov-Krasovskii functional with triple integral terms and implementation of the property of Kronecker product together with some well known matrix inequality techniques, a mean square consensus for mixed delay multi-agent system can be achieved. Terminally, two numerical examples are provided to illuminate the advantages of the suggested techniques.

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


  1. [1]

    J. Lin, A. S. Morse, and B. D. O. Anderson, “The multi-agent Rendezvous problem,” Proc. of IEEE Conference on Decision and Control, vol. 2, pp. 1508–1513, March 2003.

    Google Scholar 

  2. [2]

    F. Zhang, H. Zhang, C. Tan, W. Wang, and J. Gao, “A new approach to distributed control for multi-agent systems based on approximate upper and lower bounds,” Int J Control Autom Syst., vol. 15, pp. 2507–2515, September 2017.

    Article  Google Scholar 

  3. [3]

    K. H. Movric and F. L. Lewis, “Cooperative optimal control for multi-agent systems on directed graph topologies,” IEEE Trans. Automat. Control, vol. 59, pp. 769–774, July 2013.

    MathSciNet  Article  Google Scholar 

  4. [4]

    T. H. Lee, J. H. Park, D. H. Ji, and H. Y. Jung, “Leader-following consensus problem of heterogeneous multi-agent systems with nonlinear dynamics using fuzzy disturbance observer,” Complexity, vol. 19, pp. 20–31, March 2014.

    MathSciNet  Article  Google Scholar 

  5. [5]

    W. Liu, S. Zhou, and X. Wu, “Leaderless consensus of multi-agent systems with Lipschitz nonlinear dynamics and switching topologies,” Neurocomputing, vol. 173, pp. 1322–1329, January 2016.

    Article  Google Scholar 

  6. [6]

    H. Su, G. Chen, X. Wang, and Z. Lin, “Adaptive secon-dorder consensus of networked mobile agents with nonlinear dynamics,” Automatica, vol. 47, pp. 368–375, February 2011.

    Article  Google Scholar 

  7. [7]

    M. Syed Ali, K. Meenakshi, and N. Gunasekaran, “Finite-time H∞ boundedness of discrete-time neural networks normbounded disturbances with time-varying delay,” Int. J. Control Autom Syst., vol. 15, pp. 2681–2689, December 2017.

    Article  Google Scholar 

  8. [8]

    F. P. Silva, V. J. S. Leite, E. B. Castelan, and G. Feng, “Delay dependent local stabilization conditions for time-delay nonlinear discrete-time systems using Takagi-Sugeno models,” Int. J. Control Autom Syst., vol. 16, pp. 1435–1447, May 2018.

    Article  Google Scholar 

  9. [9]

    K. Ratnavelu, M. Manikandan, and P. Balasubramaniam, “Synchronization of fuzzy bidirectional associative memory neural networks with various time delays,” Appl Math Comput, vol. 270, pp. 582–605, November 2015.

    MathSciNet  MATH  Google Scholar 

  10. [10]

    X. Zhang, X. Zhang, D. Li, and D. Yang, “Adaptive synchronization for a class of fractional order time-delay uncertain chaotic systems via fuzzy fractional order neural network,” Int. J. Control Autom Syst., vol. 17, pp. 1209–1220, May 2019.

    Article  Google Scholar 

  11. [11]

    F. Wang and Y. Q. Yang, “Leader-following exponential consensus of fractional order nonlinear multi-agents system with hybrid time-varying delay: A heterogeneous impulsive method,” Physica A, vol. 482, pp. 158–172, September 2017.

    MathSciNet  Article  Google Scholar 

  12. [12]

    N. L. Johnson, A. W. Kemp, and S. Kotz, Univariate Discrete Distributions, John Wiley Sons, USA, 2005.

    Google Scholar 

  13. [13]

    S. Selvi, R. Sakthivel, and K. Mathiyalagan, “Robust sampled-data control of uncertain switched neutral systems with probabilistic input delay,” Complexity, vol. 21, no. 5, pp. 308–318, May/June 2016.

    MathSciNet  Article  Google Scholar 

  14. [14]

    B. Kaviarasan, R. Sakthivel, and S. Abbas, “Robust consensus of nonlinear multi-agent systems via reliable control with probabilistic time delay,” Complexity, vol. 21, no. S2, pp. 138–150, November/December 2016.

    MathSciNet  Article  Google Scholar 

  15. [15]

    H. Li, “Leader-following consensus of nonlinear multi-agent systems with mixed delays and uncertain parameters via adaptive pinning intermittent control,” Nonlinear Analysis: Hybrid Systems, vol. 22, pp. 202–214, November 2016.

    MathSciNet  MATH  Google Scholar 

  16. [16]

    C. Ge, Ju H. Park, C. Hua, X. Guan, “Nonfragile consensus of multi-agent systems based on memory sampled-data control,” IEEE Trans. Syst., Man, and Cyber: Syst., 2018. DOI: 10.1109/TSMC.2018.2874305

    Google Scholar 

  17. [17]

    C. Ge, H. Wang, Y. Liu, and J. H. Park, “Stabilization of chaotic systems under variable sampling and state quantized controller,” Fuzzy Sets and Syst., vol. 344, pp. 129–144, 2018.

    MathSciNet  Article  Google Scholar 

  18. [18]

    C. Ge, B. Wang, J. H. Park, and C. Hua, “Improved synchronization criteria of Lur’e systems under sampled-data control,” Nonlinear Dynamics, vol. 94, pp. 2827–2839, 2018.

    Article  Google Scholar 

  19. [19]

    C. Ge, Y. Shi, J. H. Park, and C. Hua, “Robust H stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control,” Applied Mathematics and Computation, vol. 346, 500–512, 2019.

    MathSciNet  Article  Google Scholar 

  20. [20]

    X. Sui, Y. Yang, X. Xu, S. Zhang, and L. Zhang, “The sampled-data consensus of multi-agent systems with probabilistic time-varying delays and packet losses,” Physica A: Statistical Mechanics and its Applications, vol. 492, pp. 1625–1641, 2017.

    MathSciNet  Article  Google Scholar 

  21. [21]

    W. B. Zhang, Y. Tang, T. Huang, and J. Kurths, “Sampled-data consensus of linear multi-agent systems with packet losses,” IEEE Trans, on Neural Netw. and Learn. Syst., vol. 28, pp. 2516–2527, August 2016.

    MathSciNet  Article  Google Scholar 

  22. [22]

    J. Wu, Y. Shi, B. X. Mu, H. Li, and W. Li, “Average consensus in multi-agent systems with non-uniform time-varying delays and random packet losses,” IFAC, vol. 46, pp. 321–326, September 2013.

    Google Scholar 

  23. [23]

    Y. Zhang and Y. P. Tian, “Consensus of data sampled multi-agent systems with random communication delay and packet loss,” IEEE Trans. Autom. Control, vol. 55, pp. 939–943, February 2010.

    MathSciNet  Article  Google Scholar 

  24. [24]

    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,” Commun Nonlinear Sci Numer Simul, vol. 19, pp. 3184–3201, September 2014.

    MathSciNet  Article  Google Scholar 

  25. [25]

    C. Peng and Y. C. Tian, “Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay,” J. Comput. Appl. Math., vol. 214, pp. 480–494, May 2008.

    MathSciNet  Article  Google Scholar 

  26. [26]

    M. Syed Ali, N. Gunasekaran, and M. Esther Rani, “Robust stability of Hopfield delayed neural networks via an augmented L-K functional,” Neuro computing, vol. 234, pp. 198–204, April 2017.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to M. Syed Ali.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Editor Jessie (Ju H.) Park. This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (DF-518-130-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support.

M. Syed Ali is working as an Assistant Professor in Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, India. He was awarded Young Scientist Award 2016 by the Academy of Sciences, Chennai. He has published more than 140 research papers in various SCI journals holding impact factors. He has also published research articles in national journals and international conference proceedings. He also serves as a reviewer for several SCI journals. His research interests include stochastic differential equations, dynamical systems, complex networks.

R. Agalya is pursuing a Ph.D. degree in the Department of Mathematics, Thiruvalluvar University, Tamil Nadu, India. Her research interests are genetic regulatory networks, Neural networks, Multi-agent system.

Sumit Saroha is with Department of Printing Technology (Electriacal Engineering), Guru Jhambheswar university of Science and Tecchnology, Hisar, India. His research interests includes fractional order systems and Multi agent systems.

Tareq Saeed received his B.S. degrees in Mathematics from King Abdulaziz, Jeddah, Saudi Arabia, his M.S. degree in Financial Mathematics from Wollongong University, and a Ph.D. degree in Griffith University, in 2018. Currently, He is working as an Assistant Professor at the Mathematics Department, King Abdulaziz University (KAU).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Syed Ali, M., Agalya, R., Saroha, S. et al. Leaderless Consensus of Non-linear Mixed delay Multi-agent Systems with Random Packet Losses via Sampled-data Control. Int. J. Control Autom. Syst. 18, 1885–1893 (2020). https://doi.org/10.1007/s12555-019-0446-1

Download citation


  • Consensus
  • Kronecker product
  • multi-agent systems (MASs)
  • probabilistic time delay