Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Dynamic modeling of discrete leader-following consensus with impulses

Department of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 236 Bulgaria Blvd., Plovdiv 4027, Bulgaria

Special Issues: Initial and Boundary Value Problems for Differential Equations

A leader-following consensus of discrete-time multi-agent systems with nonlinear intrinsic dynamics and impulses is investigated. We propose and prove conditions ensuring a leader-following consensus. Numerical examples are given to illustrate effectiveness of the obtained results. Also, the necessity and sufficiency of the obtained conditions are shown.
  Article Metrics

Keywords neural networks; discrete models; leader-following consensus; impulses

Citation: Snezhana Hristova, Kremena Stefanova, Angel Golev. Dynamic modeling of discrete leader-following consensus with impulses. AIMS Mathematics, 2019, 4(5): 1386-1402. doi: 10.3934/math.2019.5.1386


  • 1. R. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, 2 Eds, New York: CRC Press, 2000.
  • 2. R. Agarwal, S. Hristova, A. Golev, et al., Monotone-iterative method for mixed boundary value problems for generalized difference equations with "maxima", J. Appl. Math. Comput., 43 (2013), 213-233.
  • 3. L. J. S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Math. Biosci., 124 (1994), 83-105.
  • 4. J. Almeida, C. Silvestre, A. Pascoa, Continuous-time consensus with discrete-time communications, Syst. Control Lett., 61 (2012), 788-796.
  • 5. S. Elaydi, An Introduction to Difference Equations, 3 Eds., Springer, 2005.
  • 6. W. Hu, Q. Zhu, Moment exponential stability of stochastic nonlinear delay systems with impulse effects at random times, Intern. J. Robust Nonl. Contr., 29 (2019), 3809-3820.
  • 7. G. Jing, Y. Zheng, L. Wang, Consensus of multiagent systems with distance-dependent communication networks, IEEE T. Neur. Net. Lear., 28 (2017), 2712-2726.
  • 8. W. G. Kelley, A. C. Peterson, Difference Equations: An Introduction with Applications, 2 Eds., Academic Press, 2001.
  • 9. U. Krause, A discrete nonlinear and non-autonomous model of consensus formation, Commun. Differ. Equations, 2000 (2000), 227-236.
  • 10. J. L. Li, J. H. Shen, Positive solutions for first order difference equations with impulses, Int. J. Differ. Equations, 1 (2006), 225-239.
  • 11. B. Liu, W. Lu, L. Jiao, et al., Consensus in networks of multi-agents with stochastically switching topology and time-varying delays, SIAM J. Control Optim., 56 (2018), 1884-1911.
  • 12. J. Ma, Y. Zheng, L. Wang, LQR-based optimal topology of leader following consensus, J. Robust Nonlinear Control, 25 (2015), 3404-3421.
  • 13. A. B. Malinowska, E. Schmeidel, M. Zdanowicz, Discrete leader-following consensus, Math. Meth. Appl. Sci., 40 (2017), 7307-7315.
  • 14. S. Mohamad, K. Gopalsamy, Exponential stability of continuoustime and discrete-time cellular neural networks with delays, Appl. Math. Comput., 135 (2003), 17-38.
  • 15. R. Olfati-Saber, J. Fax, R. Murray, Consensus and cooperation in networked multi-agent systems, Proc. of the IEEE, 95 (2007), 215-233.
  • 16. L. Wang, F. Xiao, A new approach to consensus problems in discrete-time multi-agent systems with time-delays, F. Sci. China Ser. F, 50 (2007), 625-635.
  • 17. W. Ni, D. Z. Cheng, Leader-following consensus of multi-agent systems under fixed and switching topologies, Syst. Control Lett., 59 (2010), 209-217.
  • 18. Z. Yu, H. Jiangn, C. Hu, Leader-following consensus of fractional-order multi-agent systems under fixed topology, Neurocomputing, 149 (2015), 613-620.
  • 19. Q. Zhu, pth Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching, J. Franklin Inst., 351 (2014), 3965-3986.
  • 20. Q. Zhu, J. Cao, Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE T. Neur. Net. Lear., 23 (2012), 467-479.
  • 21. Q. Zhu, J. Cao, R. Rakkiyappan, Exponential input-to-state stability of stochastic CohenGrossberg neural networks with mixed delays, Nonlinear Dyn., 79 (2015), 1085-1098.
  • 22. Q. Zhu, B. Song, Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays, Nonlinear Anal. Real World Appl., 12 (2011), 2851-2860.
  • 23. W. Zou, P. Shi, Z. Xiang, et al., Consensus tracking control of switched stochastic nonlinear multiagent systems via event-triggered strategy, IEEE T. Neur. Net. Lear., DOI: 10.1109/TNNLS.2019.2917137.
  • 24. W. Zou, Z. Xiang, C. K. Ahn, Mean square leader-following consensus of second-order nonlinear multi-agent systems with noises and unmodeled dynamics, IEEE T. Sys. Man Cybern., DOI: 10.1109/TSMC.2018.2862140.


Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved