Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Leader-following consensus of linear discrete-time multi-agent systems subject to jointly connected switching networks

  • 132 Accesses

  • 2 Citations


In this paper, we further study the leader-following consensus problem for a class of linear discrete-time multi-agent systems subject to jointly connected switching digraphs. We first establish a stability result for a class of linear switched systems under a more relaxed assumption than those in the literature. Then, we apply this stability result to obtain the solution to our problem, which contains previous results as special cases. Finally, we apply our result to an example that cannot be handled by any existing result.

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


  1. 1

    Chen F, Ren W, Lin Z L. Multi-leader multi-follower coordination with cohesion, dispersion, and containment control via proximity graphs. Sci China Inf Sci, 2017, 60: 110204

  2. 2

    Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control, 2004, 49: 1520–1533

  3. 3

    Qu Z H. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Berlin: Springer, 2009

  4. 4

    Ren W. Distributed attitude alignment in spacecraft formation flying. Int J Adapt Control Signal Process, 2007, 21: 95–113

  5. 5

    Ren W, Beard R W. Distributed Consensus in Multi-vehicle Cooperative Control. Berlin: Springer, 2008

  6. 6

    Lewis F L, Zhang H W, Hengster-Movric K, et al. Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches. Berlin: Springer, 2014

  7. 7

    Zhu B, Xie L H, Han D, et al. A survey on recent progress in control of swarm systems. Sci China Inf Sci, 2017, 60: 070201

  8. 8

    Tuna S E. Synchronizing linear systems via partial-state coupling. Automatica, 2008, 44: 2179–2184

  9. 9

    You K Y, Xie L H. Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans Autom Control, 2011, 56: 2262–2275

  10. 10

    Hengster-Movric K, You K Y, Lewis F L, et al. Synchronization of discrete-time multi-agent systems on graphs using Riccati design. Automatica, 2013, 49: 414–423

  11. 11

    Liu J W, Huang J. Leader-following consensus for linear discrete-time multi-agent systems subject to static networks. In: Proceedings of the 36th Chinese Control Conference (CCC), Dalian, 2017. 8684–8689

  12. 12

    Huang J. The consensus for discrete-time linear multi-agent systems under directed switching networks. IEEE Trans Autom Control, 2017, 62: 4086–4092

  13. 13

    Lee T, Xia W G, Su Y F, et al. New stability results for switched discrete-time systems with application to consensus problems. In: Proceedings of the 55th Conference on Decision and Control, Las Vegas, 2016. 5508–5514

  14. 14

    Su Y F, Huang J. Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica, 2012, 48: 1988–1997

  15. 15

    Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control, 2003, 48: 988–1001

  16. 16

    Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control, 2005, 50: 655–661

  17. 17

    Cheng D Z, Wang J H, Hu X M. An extension of LaSalle’s invariance principle and its application to multi-agent consensus. IEEE Trans Autom Control, 2008, 53: 1765–1770

Download references


This work was supported by Research Grants Council of the Hong Kong Special Administration Region (Grant No. 14200617).

Author information

Correspondence to Jie Huang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Huang, J. Leader-following consensus of linear discrete-time multi-agent systems subject to jointly connected switching networks. Sci. China Inf. Sci. 61, 112208 (2018). https://doi.org/10.1007/s11432-018-9453-x

Download citation


  • multi-agent system
  • discrete-time consensus
  • jointly connected digraphs