Couple-group consensus for second-order multi-agent systems
with fixed and stochastic switching topologies
Huanyu Zhao
a,b
, Ju H. Park
a,
⇑
, Yulin Zhang
b
a
Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea
b
Faculty of Electronic and Electrical Engineering, Huaiyin Institute of Technology, Huai’an 223003, Jiangsu, PR China
article info
Keywords:
Couple-group consensus
Multi-agent system
Fixed topology
Stochastic switching topology
abstract
This paper deals with the couple-group consensus problem for second-order discrete-time
multi-agent systems. Both the fixed topology case and the stochastic switching topology
case are considered. The couple-group consensus problem is converted into the stability
problem of the error system by a linear transformation. For the fixed topology case, we
obtain two different conditions of couple-group consensus. For the stochastic switch ing
topology case, we obtain a necessary and sufficient condition of mean-square couple-group
consensus. Algorithms are provided to design the allowable control gains. Finally, simula-
tion examples are given to show the usefulness of the theoretical results.
Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction
In the past decade, distributed cooperative control has attracted a tremendous amount of interest. As one important
branch of distributed cooperative control, the consensus problem has made a great progress [1–5]. In the early literature,
attentions were mainly focus on the single-integrator [6,7].In[6], the consensus seeking problem of multi-agent systems
with dynamically changing interaction topologies was studied, where both discrete and continuous consensus algorithms
were considered. The LMI method was used to deal with the robust H
1
consensus problem of single-order multi-agent sys-
tems with uncertainty in [7]. The consensus problem for double-integrator multi-agent systems has also attracted a lot of
attentions since the theoretical framework of consensus problem for multi-agent systems was posed [8,9].In[8], some nec-
essary and sufficient conditions of consensus for second-order multi-agent systems were obtained, where the systems with
communication delays also were considered. In [9], the second-order consensus problem of multi-agent systems with inher-
ent delayed nonlinear dynamics and intermittent communications was studied.
Recently, the multi-agent systems with fixed topology have been extended to switching topology scenario [10,11].In[10],
second-order consensus problem of multi-agent systems with switching topology and communication delay was studied,
where the switching signal was arbitrary and the every topology was connected. In [11], the authors studied the finite-time
consensus problem for second-order networked multi-agent systems with an undirected switching graph. However, the
switching topologies are in the deterministic framework in the above literature. Some consensus results for multi-agent sys-
tems with stochastic switching topologies have been obtained [12–14].In[12], the authors studied the mean square con-
sensusability problem for a network of double-integrator agents with Markov switching topologies. While in [14],an
observer-based control strategy for networked multi-agent systems with communication delay and stochastic switching
http://dx.doi.org/10.1016/j.amc.2014.01.018
0096-3003/Ó 2014 Elsevier Inc. All rights reserved.
⇑
Corresponding author.
E-mail addresses: hyzhao10@gmail.com (H. Zhao), jessie@ynu.ac.kr (J.H. Park).
Applied Mathematics and Computation 232 (2014) 595–605
Contents lists available at ScienceDirect
Applied Mathematics and Computation
journal homepage: www.elsevier.com/locate/amc
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