Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2665–2677 | Cite as

Further Results on Containment Control for Multi-Agent Systems with Variable Communication Delay

  • Zhipeng Li
  • Tao LiEmail author
  • Ruiting Yuan
  • Shumin Fei
Research Article - Systems Engineering


This paper considers the problem on containment control of general linear multi-agent systems (MASs) with communication time-varying delay. Based on directed interaction topology, some sufficient conditions on the existence of feedback controller gains are provided to ensure the desired control. Through choosing an augmented Lyapunov–Krasovskii (K–L) functional and using some novel integral inequalities to estimate the derivative of Lyapunov functional, the previously ignored information can be reconsidered and the application area of the derived results can be greatly extended. Moreover, a novel constructive method is proposed to compute out the controller gains based on LMI technique. Finally, a numerical example with some simulations is provided to illustrate the effectiveness of the obtained results.


Containment control General linear multi-agent systems Time-varying delay LMI technique 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ferrari-Trecate, G.; Egerstedt, M.; Buffa, A.; Ji, M.: A hybrid stop-go policy for leader-based containment control. In: Hybrid Systems Computation and Control, pp. 212–226 (2006)Google Scholar
  2. 2.
    Deng, C.; Yang, G.H.: Distributed adaptive fault-tolerant containment control for a class of multi-agent systems with non-identical matching non-linear functions. IET Control Theory Appl. 10(3), 273–281 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ma, L.; Min, H.; Wang, S.; et al.: Distributed containment control of networked nonlinear second-order systems with unknown parameters. IEEE/CAA J. Automat. Sin. 99, 1–9 (2016)Google Scholar
  4. 4.
    Zhou, H.; Ji, Y.; Gao, S.; et al.: Distributed containment control for multiple-agent systems in nonlinear pure-feedback form via singular perturbation analysis. In: IEEE Conference on Control and Decision, pp. 2319–2324 (2016)Google Scholar
  5. 5.
    Hu, J.; Yu, J.; Cao, J.: Distributed containment control for nonlinear multi-agent systems with time-delayed protocol. Asian J. Control 18(2), 747–756 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Huang, N.; Duan, Z.; Yu, C.: Distributed event-triggered containment control of multiple rigid bodies with combinational measurements. In: IEEE International Conference on Control, Automation, Robotics and Vision, pp. 1–6 (2017)Google Scholar
  7. 7.
    Sun, Y.; Li, Z.; Ma, D.: Event-based finite time containment control for multi-agent systems. In: The 31st Youth Academic Annual Conference of Chinese Association, pp. 129–134 (2017)Google Scholar
  8. 8.
    Zhang, W.; Tang, Y.; Liu, Y.: Event-triggering containment control for a class of multi-agent networks with fixed and switching topologies. IEEE Trans. Circuits Syst. 64(3), 619–629 (2017)CrossRefGoogle Scholar
  9. 9.
    Han, T.; Chi, M.; Guan, Z.; et al.: Distributed three-dimensional formation containment control of multiple unmanned aerial vehicle systems. Asian J. Control 19(3), 157–163 (2017)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Meng, Y.Z.; Ren, W.; You, Z.: Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46(12), 2092–2099 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Peng, X.; Geng, Z.; Tayefi, M.: Containment control based formation tracking for multi-vehicles on lie group. In: Chinese Control Conference, pp. 7751–7756 (2016)Google Scholar
  12. 12.
    Cao, H.Z.; Yan, X.; Zhou, F.: Research on containment control of second-order nonlinear multi-agent with collision avoidance mechanism. Acta Armamentarii 9, 1646–1654 (2016)Google Scholar
  13. 13.
    Zhen, K.; She, J.M.; Dixon, W.E.: Leader–follower containment control over directed random graphs. Automatica 66(C), 56–62 (2016)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Han, L.; Dong, X.W.; Li, Q.: Formation-containment control for second-order multi-agent systems with time-varying delays. Neurocomputing 218, 439–447 (2016)CrossRefGoogle Scholar
  15. 15.
    Ji, H.; Zhang, H.; Cui, B.: Containment analysis of Markov jump swarm systems with stationary distribution. IET Control Theory Appl. 11(7), 901–907 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wang, F.; Yang, H.; Liu, Z.: Second-order containment control of multi-agent systems in the presence of uncertain topologies with time-varying delays. J. Control Sci. Eng.
  17. 17.
    Li, B.; Chen, Z.Q.; Liu, Z.X.: Containment control of multi-agent systems with fixed time-delays in fixed directed networks. Neurocomputing 173(P3), 2069–2075 (2016)CrossRefGoogle Scholar
  18. 18.
    Wang, F.; Yang, H.; Liu, Z.: Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays. Neurocomputing 260(80), 341–348 (2017)CrossRefGoogle Scholar
  19. 19.
    Liu, Y.; Zhao, Y.; Shi, Z.: Specified-time containment control of multi-agent systems over directed topologies. IET Control Theory Appl. 11(4), 576–585 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Li, B.; Chen, Q.Z.; Zhang, C.Y.: Containment control for directed networks multi-agent system with nonlinear dynamics and communication time-delays. Int. J. Control Autom. Syst. 15(3), 1181–1188 (2017)CrossRefGoogle Scholar
  21. 21.
    Liu, S.; Xie, L.; Zhang, H.: Containment control of discrete-time multi-agent systems based on delayed neighbours’ information. In: The 9th Asian Control Conference, pp. 1–6 (2013)Google Scholar
  22. 22.
    Xie, X.; Yang, Z.; Fang, J.: Containment control of multi-agent systems with input saturation and intermittent communication. In: The 31st Youth Academic Annual Conference of Chinese Association, pp. 99–104 (2017)Google Scholar
  23. 23.
    Dong, X.W.; Shi, Z.; Lu, G.; et al.: Output containment control for high-order linear time-invariant swarm systems. Systems 8215(2), 285–290 (2013)Google Scholar
  24. 24.
    Li, Z.G.; Huang, W.P.; Du, Y.J.: H\(\infty \) containment control for second-order multi-agent systems with time delay. In: Chinese Control Conference, pp. 7926–7931 (2016)Google Scholar
  25. 25.
    Liao, F.C.; Kong, M.; Liu, H.Y.: H\(\infty \) containment control for first-order multi-agent systems with multiple time-varying delays. Control Decis. 32(4), 584–592 (2017)zbMATHGoogle Scholar
  26. 26.
    Jia, Y.: Robust H\(\infty \) containment control for uncertain multi-agent systems with inherent nonlinear dynamics. Int. J. Syst. Sci. 47(5), 1–11 (2016)MathSciNetGoogle Scholar
  27. 27.
    Wang, D.; Zhang, N.; Wang, J.; et al.: Cooperative containment control of multiagent systems based on follower observers with time delay. IEEE Trans. Syst. Man Cybern. Syst. 99, 1–11 (2016)Google Scholar
  28. 28.
    Yang, Z.; Mu, X.; Liu, K.: Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies. Int. J. Control Autom. Syst. 15(1), 442–449 (2017)CrossRefGoogle Scholar
  29. 29.
    Dong, X.W.; Han, L.; Li, Q.; et al.: Containment analysis and design for general linear multi-agent systems with time-varying delays. Neurocomputing 173(3), 2062–2068 (2016)CrossRefGoogle Scholar
  30. 30.
    Xi, J.; Shi, Z.; Zhong, Y.: Consensus analysis and design for high-order linear swarm systems with time-varying delays. Phys. A Stat. Mech. Appl. 390(2324), 4114–4123 (2011)CrossRefGoogle Scholar
  31. 31.
    Dong, X.W.; Li, Q.D.; Zhang, R.; Zhong, Y.S.: Formation-containment control for high-order linear time-invariant multi-agent systems with time delays. J. Frankl. Inst. 352(9), 3564–3584 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Wang, X.L.; et al.: Second-order consensus of multi-agent systems via periodically intermittent pinning control. Circuits Syst. Signal Process. 35(7), 2413–2431 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Zhong, Z.; Sun, L.; Wang, J.; et al.: Consensus for first- and second-order discrete-time multi-agent systems with delays based on model predictive control schemes. Circuits Syst. Signal Process. 34(1), 127–152 (2015)CrossRefzbMATHGoogle Scholar
  34. 34.
    Zeng, H.; He, Y.; Wu, M.; She, J.H.: New results on stability analysis for systems with discrete distributed delay. Automatica 63, 189–192 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Liu, Y.; Ju, H.P.; Guo, B.Z.: Results on stability of linear systems with time varying delay. IET Control Theory Appl. 11(1), 129–134 (2016)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Park, M.; Kwon, O.; Park, J.H.; Lee, S.: Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55, 204–208 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Park, P.; Lee, W.; Lee, S.Y.: Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J. Frankl. Inst. 352(4), 1378–1396 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Hua, C.C.; Wu, S.S.; Yang, X.; Guan, X.P.: Stability analysis of time-delay systems via free-matrix-based double integral inequality. Int. J. Syst. Sci. 48(2), 257–263 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Zhang, C.K.; He, Y.; Jiang, L.; Wu, M.; Zeng, H.B.: Stability analysis of systems with time-varying delay via relaxed integral inequalities. Syst. Control Lett. 92, 52–61 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Li, T.; Wang, T.; Song, A.G.; Fei, S.M.: Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay. IEEE Trans. Neural Netw. 21, 1365–1371 (2010)CrossRefGoogle Scholar
  41. 41.
    Shen, M.Q.; Yan, S.; Zhang, G.M.: A new approach to event-triggered static output feedback control of networked control systems. ISA Trans. 65(4), 468–474 (2016)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of AutomationSoutheast UniversityNanjingChina

Personalised recommendations