This paper considers the leader-following consensus problem for nonlinear multiagent systems with large delays. The time delays switch alternately between two different kinds of delays, called a small delay and a large delay. New Lyapunov functionals that depend on graph information are constructed. To guarantee the desired leader-following consensus, the concepts of the length and frequency of the large delay periods are introduced. Sufficient conditions for consensus are given in terms of linear matrix inequalities. Furthermore, low-dimensional criteria that are easily implemented especially for large-scale multiagent systems are provided. Finally, two simulation examples are presented to validate the effectiveness of the proposed scheme.
BenderJG (1991) An overview of systems studies of automated highway systems. IEEE Transactions on Vehicular Technology40(1): 82–99.
2.
CaoMMorseASAndersonBD (2008) Reaching a consensus in a dynamically changing environment: A graphical approach. SIAM Journal on Control and Optimization47(2): 575–600.
3.
ChenCPWenGXLiuYJWangFY (2014) Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Transactions on Neural Networks and Learning Systems25(6): 1217–1226.
4.
ChuHZhangW (2016) Adaptive consensus tracking for linear multi-agent systems with input saturation. Transactions of the Institute of Measurement and Control38(12): 1434–1441.
5.
DingLGuoG (2015) Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay. Journal of the Franklin Institute352(1): 369–383.
DuSLWangRWangSYuM (2016) Observer-based H∞ stabilisation for linear systems with large delay periods. IET Control Theory & Applications10(4): 417–423.
8.
DuSLXiaWRenWSunXMWangW (2017a) Observer-based consensus for multiagent systems under stochastic sampling mechanism. IEEE Transactions on Sytems, Man and Cybernetics: Systems. DOI:10.1109/TSMC.2017.2703137.
9.
DuSLXiaWSunXMWangW (2017b) Sampled-data-based consensus and L2 gain analysis for heterogeneous multiagent systems. IEEE Transactions on Cybernetics47(6): 1523–1531.
10.
HeWChenGHanQLQianF (2017a) Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. Information Sciences380: 145–158.
11.
HeWZhangBHanQLQianFKurthsJCaoJ (2017b) Leader-following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Transactions on Cybernetics47(2): 327–338.
12.
HongYHuJGaoL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica42(7): 1177–1182.
13.
HornRJohnsonC (1991) Topics in Matrix Analysis. Cambridge: Cambridge University Presss.
14.
HuJCaoJ (2017) Consensus seeking for multi-agent systems by hybrid output feedback protocol. Transactions of the Institute of Measurement and Control39(7): 1104–1113.
15.
JadbabaieALinJMorseAS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic control48(6): 988–1001.
16.
JiaQTangWK (2012) Consensus of nonlinear agents in directed network with switching topology and communication delay. IEEE Transactions on Circuits and Systems I: Regular Papers59(12): 3015–3023.
17.
LiHLiaoXLeiXHuangTZhuW (2013) Second-order consensus seeking in multi-agent systems with nonlinear dynamics over random switching directed networks. IEEE Transactions on Circuits and Systems I: Regular Papers60(6): 1595–1607.
18.
LiXRakkiyappanRSakthivelN (2015) Non-fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time-varying coupling delays. Asian Journal of Control17(5): 1678–1695.
19.
LiXSongS (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Transactions on Neural Networks and Learning Systems24(6): 868–877.
20.
LiXWangRWuSNDimirovskiGM (2017) Exponential stability for multi-area power systems with time delays under load frequency controller failures. Asian Journal of Control19(2): 787–791.
21.
LinPJiaY (2009) Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica45(9): 2154–2158.
22.
LinPJiaY (2010) Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies. IEEE Transactions on Automatic Control55(3): 778–784.
23.
LiuBHillDJSunZ (2018a) Input-to-state exponents and related ISS for delayed discrete-time systems with application to impulsive effects. International Journal of Robust & Nonlinear Control28(2): 640–660.
24.
LiuBHillDJSunZ (2018b) Input-to-state-stability and criteria for a class of hybrid dynamical systems. Applied Mathematics & Computation326: 124–140.
25.
LiuHKarimiHRDuSXiaWZhongC (2017) Leader-following consensus of discrete-time multiagent systems with time-varying delay based on large delay theory. Information Sciences417: 236–246.
26.
LuJHoDWCaoJ (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica46(7): 1215–1221.
27.
Olfati-SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
28.
RenWBeardRW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control50(5): 655–661.
29.
RenWBeardRAtkinsE (2007) Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine2(27): 71–82.
30.
SongQCaoJLiuF (2012) Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays. International Journal of Robust and Nonlinear Control22(6): 690–706.
31.
StrogatzSHStewartI (1993) Coupled oscillators and biological synchronization. Scientific American269: 68–68.
32.
SunXMLiuGPReesDWangW (2008) Delay-dependent stability for discrete systems with large delay sequence based on switching techniques. Automatica44(11): 2902–2908.
33.
WangRLiXZhouWY (2015) Guaranteed cost load frequency control for a class of uncertain power systems with large delay periods. Neurocomputing168: 269–275.
34.
WangRSunYT (2013) Stability analysis of linear descriptor systems with large delay period. In: 2013 32nd Chinese Control Conference (CCC). IEEE, pp. 2120–2125.
35.
WangZXuJZhangH (2014) Consensusability of multi-agent systems with time-varying communication delay. Systems & Control Letters65: 37–42.
36.
WenGDuanZChenGYuW (2014) Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies. IEEE Transactions on Circuits and Systems I: Regular Papers61(2): 499–511.
37.
WenGDuanZYuWChenG (2013) Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach. International Journal of Robust and Nonlinear Control23(6): 602–619.
38.
XiaoFWangL (2008) Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays. IEEE Transactions on Automatic Control53(8): 1804–1816.
39.
XuWCaoJYuWLuJ (2014) Leader-following consensus of non-linear multi-agent systems with jointly connected topology. IET Control Theory & Applications8(6): 432–440.
40.
YuWZhengWXChenGRenWCaoJ (2011) Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica47(7): 1496–1503.
41.
YuanDHoDWXuS (2016) Regularized primal–dual subgradient method for distributed constrained optimization. IEEE Transactions on Cybernetics46(9): 2109–2118.
42.
ZhangGXuJZengJXiJTangW (2017) Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays. Transactions of the Institute of Measurement and Control39(8): 1182–1194.
43.
ZhangYTianYP (2010) Consensus of data-sampled multi-agent systems with random communication delay and packet loss. IEEE Transactions on Automatic Control55(4): 939–943.
44.
ZhaoXYinYNiuBZhengX (2016a) Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling. IEEE Transactions on Cybernetics46(8): 1952–1957.
45.
ZhaoXYinYZhengX (2016b) State-dependent switching control of switched positive fractional-order systems. ISA Transactions62: 103–108.
46.
ZhouBLiaoX (2014) Leader-following second-order consensus in multi-agent systems with sampled data via pinning control. Nonlinear Dynamics78(1): 555–569.
