This paper considers a consensus control of a general linear multi-agent system with time-varying communication delays. Since each agent can only use the relative output information from its neighbors, a reduced-order observer-based control protocol is proposed to guarantee consensus on the directed communication network. The stability of the closed-loop system is analyzed for the cases with uniform delays and nonuniform time-varying delays, respectively. Moreover, the upper bounds of the communication delays are obtained respectively for the two cases. Finally, two numerical examples are provided to illustrate the proposed theoretical results.
ChenLQinKHuJ (2018) Bounded consensus tracking control of second-order multi-agent systems with active leader and jointly connected topology. Transactions of the Institute of Measurement and Control40(2): 504–513.
2.
ChenYShiY (2017) Consensus for linear multiagent systems with time-varying delays: A frequency domain perspective. IEEE Transactions on Cybernetics47(8): 2143–2150.
3.
DegrootM (1974) Reaching a consensus, Journal of the American Statistical Association69(345): 118–121.
4.
DingLHanQWangLSindiE (2018) Distributed cooperative optimal control of DC microgrids with communication delays. IEEE Transactions on Industrial Informatics14(9): 3924–3935.
5.
DongXYuBShiZZhongY (2015) Time-varying formation control for unmanned aerial vehicles: Theories and applications. IEEE Transactions on Control Systems Technology23(1): 340–348.
6.
DongYHuangJ (2015) Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law. Automatica55(5): 197–203.
7.
DuSXiaWRenW, et al. (2018) Observer-based consensus for multiagent systems under stochastic sampling mechanism. IEEE Transactions on Systems, Man, and Cybernetics: Systems48(12): 2328–2338.
8.
FanYHuangXShenHCaoJ (2019) Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme. Neural Networks117: 216–224.
9.
FengZSunCHuG (2017) Robust connectivity preserving rendezvous of multirobot systems under unknown dynamics and disturbances. IEEE Transactions on Control of Network Systems4(4): 725–735.
10.
GaoLXuBLiJZhangH (2015) Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems. IET Control Theory & Applications9(5): 784–792.
11.
HouWFuMZhangHWuZ (2017) Consensus conditions for general second-order multi-agent systems with communication delay. Automatica75: 293–298.
12.
HuJHongY (2007) Leader-following coordination of multi-agent systems with coupling time delays. Physica A Statistical Mechanics & Its Applications374(2): 853–863.
13.
HuJLinYS (2010) Consensus control for multi-agent systems with double-integrator dynamics and time delays. IET Control Theory & Applications4(1): 109–118.
14.
HuangCZhaiGXuG (2018) Necessary and sufficient conditions for consensus in third order multi-agent systems. IEEE/CAA Journal of Automatica Sinica5(6): 1044–1053.
15.
JadbabaieALinJMorseAS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor. IEEE Transactions on Automatic Control48(6): 988–1001.
16.
JafarpourSBulloF (2019) Synchronization of kuramoto oscillators via cutset projections. IEEE Transactions on Automatic Control64(7): 2830–2844.
17.
LiLFuMZhangHLuR (2018) Consensus control for a network of high order continuous-time agents with communication delays. Automatica89: 144–150.
18.
LiPXiongQYangC (2019) Containment control for high-order multi-agent systems with nonuniform communication delays and switching topologies. IEEE Access7: 47577–47581.
19.
LiXSohYCXieL (2019) A novel reduced-order protocol for consensus control of linear multi-agent systems. IEEE Transactions on Automatic Control64(7): 3005–3012.
20.
LiZDuanZChenGHuangL (2010) Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Transactions on Circuits & Systems I Regular Papers57(1): 213–224.
21.
LiZLiuXLinPRenW (2011) Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems & Control Letters60(7): 510–516.
22.
Olfati-SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
23.
QianWGaoYYangY (2018) Global consensus of multiagent systems with internal delays and communication delays. IEEE Transactions on Systems, Man, and Cybernetics: Systems49(10): 1961–1970.
24.
RenWBeardRW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control50 (5): 655–661.
25.
ReynoldsC W (1987) Flocks, herds and schools: A distributed behavioral model. SIGGRAPH Comput. Graph21(4): 25–34.
26.
SavinoH Jdos SantosCRPSouzaFO, et al. (2016) Conditions for consensus of multi-agent systems with time-delays and uncertain switching topology. IEEE Transactions on Industrial Electronics63(2): 1258–1267.
27.
ShiMQinKLiPLiuJ (2017) Consensus conditions for high-order multiagent systems with nonuniform delays. Mathematical Problems in Engineering2017: 7307834 (12 pages).
28.
TangZHuangTShaoJHuJ (2012) Consensus of second-order multi-agent systems with nonuniform time-varying delays. Neurocomputing97(11): 410–414.
29.
VicsekTCzirokABen-JacobE, et al. (1995) Novel type of phase transition in a system of self-driven particles. Physical Review Letters75(6): 1226–1229.
30.
WangXShiLShaoJ (2018) Containment control for high-order multi-agent systems with heterogeneous time delays. ISA Transactions12(9): 1340–1348.
31.
WangXWangZSongQ, et al. (2020) A waiting-time-based event-triggered scheme for stabilization of complex-valued neural networks. Neural Networks121: 329–338.
32.
WangYGuYXieXZhangH (2019) Delay-dependent distributed event-triggered tracking control for multi-agent systems with input time delay. Neurocomputing333: 200–210.
33.
WangZHeMZhengT, et al. (2018) Guaranteed cost consensus for high-dimensional multi-agent systems with time-varying delays. IEEE/CAA Journal of Automatica Sinica5(1): 181–189.
34.
XiaoWWangRDongX, et al. (2018) Time-varying formation control for general linear multi-agent systems with time-varying delays and switching topologies. In: 2018 IEEE 14th International Conference on Control and Automation (ICCA), Anchorage, AK, USA, 12–15 June 2018, pp. 16–21. IEEE.
35.
YanZGaoLTongC (2013) On distributed reduced-order observer-based protocol for linear multiagent consensus under switching topology. Abstract and Applied Analysis2013(5): 112–128.
36.
ZhaoDDongT (2017) Reduced-order observer-based consensus for multi-agent systems with time delay and event trigger strategy. IEEE Access5: 1263–1271.
37.
ZhengDZ (2002) Linear System Theory. Bejing: Tsinghua University Publishing House/Springer.
38.
ZhuWChengD (2010) Leader-following consensus of second-order agents with multiple time-varying delays. Automatica46(12): 1994–1999.
