Abstract

The existing results on the leader-following consensus problem for linear continuous-time multi-agent systems over jointly connected switching digraphs rely on the assumption that the system matrices do not have eigenvalues with positive real parts. In this paper, to remove this assumption, we first establish a stability result for a class of linear switched systems. Then, we show that the leader-following consensus problem for linear multi-agent systems with general system modes over jointly connected switching digraphs is solvable if the digraphs are acyclic. Moreover, the leader-following consensus can be achieved at a pre-assigned but arbitrarily fast convergence rate. A numerical example is provided to illustrate our design.

References

References
1.
Su
,
S.
, and
Lin
,
Z.
,
2016
, “
Distributed Consensus Control of Multi-Agent Systems With Higher Order Agent Dynamics and Dynamically Changing Directed Interaction Topologies
,”
IEEE Trans. Autom. Control
,
61
(
2
), pp.
515
519
.10.1109/TAC.2015.2444211
2.
Liu
,
Z.
,
Zhang
,
M.
,
Saberi
,
A.
, and
Stoorvogel
,
A. A.
,
2018
, “
State Synchronization of Multi-Agent Systems Via Static or Adaptive Nonlinear Dynamic Protocols
,”
Automatica
,
95
, pp.
316
327
.10.1016/j.automatica.2018.05.034
3.
Meng
,
H.
,
Chen
,
Z.
, and
Middleton
,
R.
,
2018
, “
Consensus of Multiagents in Switching Networks Using Input-to-State Stability of Switched Systems
,”
IEEE Trans. Autom. Control
,
63
(
11
), pp.
3964
3971
.10.1109/TAC.2018.2809454
4.
Wang
,
X.
,
Zhu
,
J.
, and
Feng
,
J.
,
2019
, “
A New Characteristic of Switching Topology and Synchronization of Linear Multiagent Systems
,”
IEEE Trans. Autom. Control
,
64
(
7
), pp.
2697
2711
.10.1109/TAC.2018.2869478
5.
Ni
,
W.
, and
Cheng
,
D.
,
2010
, “
Leader-Following Consensus of Multi-Agent Systems Under Fixed and Switching Topologies
,”
Syst. Control Lett.
,
59
(
3–4
), pp.
209
217
.10.1016/j.sysconle.2010.01.006
6.
Su
,
Y.
, and
Huang
,
J.
,
2012
, “
Stability of a Class of Linear Switching Systems With Applications to Two Consensus Problems
,”
IEEE Trans. Autom. Control
,
57
(
6
), pp.
1420
1430
.10.1109/TAC.2011.2176391
7.
Zhao
,
Z.
, and
Lin
,
Z.
,
2016
, “
Global Leader-Following Consensus of a Group of General Linear Systems Using Bounded Controls
,”
Automatica
,
68
, pp.
294
304
.10.1016/j.automatica.2016.01.027
8.
Su
,
Y.
, and
Huang
,
J.
,
2012
, “
Cooperative Output Regulation of Linear Multi-Agent Systems
,”
IEEE Trans. Autom. Control
,
57
(
4
), pp.
1062
1066
.10.1109/TAC.2011.2169618
9.
Sun
,
Z.
, and
Ge
,
S. S.
,
2005
,
Switched Linear Systems: Control and Design
,
Springer-Verlag
,
London
.
10.
Lin
,
H.
, and
Antsaklis
,
P. J.
,
2009
, “
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
,”
IEEE Trans. Autom. Control
,
54
(
2
), pp.
308
322
.10.1109/TAC.2008.2012009
11.
Ren
,
W.
, and
Beard
,
R. W.
,
2005
, “
Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies
,”
IEEE Trans. Autom. Control
,
50
(
5
), pp.
655
661
.10.1109/TAC.2005.846556
12.
Jadbabaie
,
A.
,
Lin
,
J.
, and
Morse
,
A. S.
,
2003
, “
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
,”
IEEE Trans. Autom. Control
,
48
(
6
), pp.
988
1001
.10.1109/TAC.2003.812781
13.
Qin
,
J.
, and
Yu
,
C.
,
2014
, “
Exponential Consensus of General Linear Multi-Agent Systems Under Directed Dynamic Topology
,”
Automatica
,
50
(
9
), pp.
2327
2333
.10.1016/j.automatica.2014.07.009
14.
Tanner
,
H. G.
,
Pappas
,
G. J.
, and
Kumar
,
V.
,
2004
, “
Leader-to-Formation Stability
,”
IEEE Trans. Rob. Autom.
,
20
(
3
), pp.
443
455
.10.1109/TRA.2004.825275
15.
Wang
,
X.
,
Hong
,
Y.
,
Huang
,
J.
, and
Jiang
,
Z.
,
2010
, “
A Distributed Control Approach to a Robust Output Regulation Problem for Multi-Agent Linear Systems
,”
IEEE Trans. Autom. Control
,
55
(
12
), pp.
2891
2895
.10.1109/TAC.2010.2076250
16.
Ding
,
W.
,
Yan
,
G.
, and
Lin
,
Z.
,
2010
, “
Collective Motions and Formations Under Pursuit Strategies on Directed Acyclic Graphs
,”
Automatica
,
46
(
1
), pp.
174
181
.10.1016/j.automatica.2009.10.025
17.
Qin
,
J.
, and
Yu
,
C.
,
2013
, “
Cluster Consensus Control of Generic Linear Multi-Agent Systems Under Directed Topology With Acyclic Partition
,”
Automatica
,
49
(
9
), pp.
2898
2905
.10.1016/j.automatica.2013.06.017
18.
Zhang
,
H.
,
Chen
,
Z.
, and
Mo
,
X.
,
2017
, “
Effect of Adding Edges to Consensus Networks With Directed Acyclic Graphs
,”
IEEE Trans. Autom. Control
,
62
(
9
), pp.
4891
4897
.10.1109/TAC.2017.2692527
19.
Su
,
Y.
, and
Huang
,
J.
,
2012
, “
Cooperative Output Regulation With Application to Multi-Agent Consensus Under Switching Network
,”
IEEE Trans. Syst., Man, Cybern., Part B
,
42
(
3
), pp.
864
875
.10.1109/TSMCB.2011.2179981
20.
Shi
,
G.
, and
Johansson
,
K. H.
,
2013
, “
Robust Consensus for Continuous-Time Multiagent Dynamics
,”
SIAM J. Control Optim.
,
51
(
5
), pp.
3673
3691
.10.1137/110841308
21.
Sastry
,
S.
, and
Bodson
,
M.
,
1989
,
Adaptive Control: Stability, Convergence and Robustness
,
Prentice Hall
,
Englewood Cliffs, NJ
.
22.
Liberzon
,
D.
,
2003
,
Switching in Systems and Control
,
Birkhauser
,
Boston, MA
.
23.
Callier
,
F. M.
, and
Desoer
,
C. A.
,
1991
,
Linear System Theory
,
Springer-Verlag
,
New York
.
24.
He
,
C.
, and
Huang
,
J.
,
2020
, “
Distributed Observer for General Linear Leader Systems Over Periodic Switching Digraphs
,”
Proceedings of the 39th Chinese Control Conference
, Shenyang, China, July 27–29, pp.
4853
4858
. 10.23919/CCC50068.2020.9189679
You do not currently have access to this content.