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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7307834, 12 pages
https://doi.org/10.1155/2017/7307834
Research Article

Consensus Conditions for High-Order Multiagent Systems with Nonuniform Delays

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Kaiyu Qin

Received 20 May 2016; Revised 8 October 2016; Accepted 16 October 2016; Published 9 April 2017

Academic Editor: Guido Ala

Copyright © 2017 Mengji Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. Li, G. Wen, Z. Duan, and W. Ren, “Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs,” IEEE Transactions on Automatic Control, vol. 60, no. 4, pp. 1152–1157, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. Z. Li, W. Ren, X. Liu, and M. Fu, “Consensus of multi-agent systems with general linear and lipschitz nonlinear dynamics using distributed adaptive protocols,” IEEE Transactions on Automatic Control, vol. 58, no. 7, pp. 1786–1791, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. G. Zhang, J. Xu, J. Zeng, J. Xi, and W. Tang, “Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays,” Transactions of the Institute of Measurement and Control, 2016. View at Publisher · View at Google Scholar
  4. C. Sun, G. Hu, and L. Xie, “Robust consensus tracking for a class of high-order multi-agent systems,” International Journal of Robust and Nonlinear Control, vol. 26, no. 3, pp. 578–598, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. X. Dong, Z. Shi, G. Lu, and Y. Zhong, “Time-varying output formation control for high-order linear time-invariant swarm systems,” Information Sciences, vol. 298, pp. 36–52, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. C.-C. Hua, X. You, and X.-P. Guan, “Leader-following consensus for a class of high-order nonlinear multi-agent systems,” Automatica, vol. 73, pp. 138–144, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  7. W. Ren, K. Moore, and Y.-Q. Chen, “High-order consensus algorithms in cooperative vehicle systems,” in Proceedings of the IEEE International Conference on Networking, Sensing and Control (ICNSC '06), pp. 457–462, Ft. Lauderdale, Fla, USA, April 2006. View at Scopus
  8. P. Lin, Z. Li, Y. Jia, and M. Sun, “High-order multi-agent consensus with dynamically changing topologies and time-delays,” IET Control Theory and Applications, vol. 5, no. 8, pp. 976–981, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. Q.-J. Zhang, Y.-F. Niu, L. Wang, L.-C. Shen, and H.-Y. Zhu, “Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays,” International Journal of Control, Automation and Systems, vol. 9, no. 6, pp. 1209–1218, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Wen, Z. Duan, W. Yu, and G. Chen, “Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications,” International Journal of Control, vol. 86, no. 2, pp. 322–331, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. P. Lin and Y. Jia, “Multi-agent consensus with diverse time-delays and jointly-connected topologies,” Automatica, vol. 47, no. 4, pp. 848–856, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. W. Yu, G. Chen, M. Cao, and W. Ren, “Delay-induced consensus and quasi-consensus in multi-agent dynamical systems,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 10, pp. 2679–2687, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Y.-P. Tian and C.-L. Liu, “Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations,” Automatica, vol. 45, no. 5, pp. 1347–1353, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. P.-A. Bliman and G. Ferrari-Trecate, “Average consensus problems in networks of agents with delayed communications,” Automatica, vol. 44, no. 8, pp. 1985–1995, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y.-P. Tian and C.-L. Liu, “Consensus of multi-agent systems with diverse input and communication delays,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2122–2128, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. P. Lin, Y.-M. Jia, J.-P. Du, and S.-Y. Yuan, “Distributed consensus control for second-order agents with fixed topology and time-delay,” in Proceedings of the 26th IEEE Chinese Control Conference (CCC '07), pp. 577–581, Zhangjiajie, China, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. P. Lin and Y. Jia, “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,” Automatica, vol. 45, no. 9, pp. 2154–2158, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. V. D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, “Convergence in multiagent coordination, consensus, and flocking,” in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '05), pp. 2996–3000, IEEE, 2005.
  19. U. Munz, A. Papachristodoulou, and F. Allgower, “Generalized Nyquist consensus condition for high-order linear multi-agent systems with communication delays,” in Proceedings of the 48th IEEE Conference on Decision and Control, Held Jointly with the 28th Chinese Control Conference (CDC/CCC '09), pp. 4765–4771, IEEE, Shanghai, China, December 2009. View at Publisher · View at Google Scholar
  20. U. Munz, A. Papachristodoulou, and F. Allgower, “Delay robustness in non-identical multi-agent systems,” IEEE Transactions on Automatic Control, vol. 57, no. 6, pp. 1597–1603, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. Popov and H. Werner, “Robust stability of a multi-agent system under arbitrary and time-varying communication topologies and communication delays,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2343–2347, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Fang, Z. Wu, and J. Wei, “Improvement for consensus performance of multi-agent systems based on weighted average prediction,” IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 249–254, 2012. View at Publisher · View at Google Scholar
  23. P. Lin, K.-Y. Qin, Z.-K. Li, and W. Ren, “Collective rotating motions of second-order multi-agent systems in three-dimensional space,” Systems & Control Letters, vol. 60, no. 6, pp. 365–372, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. B. Mirkin, P.-O. Gutman, and Y. Shtessel, “Asymptotic sliding mode control approach to adaptive distributed tracking problem for multi-agent nonlinear delayed systems,” International Journal of Control, vol. 85, no. 11, pp. 1671–1682, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. P. Deshpande, P. P. Menon, C. Edwards, and I. Postlethwaite, “Formation control of multi-agent systems with double integrator dynamics using delayed static output feedback,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '11), pp. 3446–3451, Orlando, Fla, USA, December 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. H. Zhang, J. Zhang, G. H. Yang, and Y. Luo, “Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 1, pp. 152–163, 2015. View at Publisher · View at Google Scholar
  27. 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, no. 4, pp. 20–31, 2014. View at Publisher · View at Google Scholar
  28. R. Ponalagusamy and S. Senthilkumar, “Investigation on numerical solution for a robot arm problem,” Journal of Automation Mobile Robotics and Intelligent Systems, vol. 3, pp. 34–40, 2009. View at Google Scholar
  29. C. P. Chen, G.-X. Wen, Y.-J. Liu, and Z. Liu, “Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems,” IEEE Transactions on Cybernetics, vol. 46, no. 7, pp. 1591–1601, 2016. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Shi and K. Qin, “Distributed control for multiagent consensus motions with nonuniform time delays,” Mathematical Problems in Engineering, vol. 2016, Article ID 3567682, 10 pages, 2016. View at Publisher · View at Google Scholar
  31. C. D. Godsil, G. Royle, and C. Godsil, Algebraic Graph Theory, vol. 8, Springer, New York, NY, USA, 2001.
  32. Y.-Y. Nie and X.-K. Xie, “New criteria for polynomial stability,” IMA Journal of Mathematical Control and Information, vol. 4, no. 1, pp. 1–12, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus