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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 254749, 7 pages
Research Article

Cluster Anticonsensus of Multiagent Systems Based on the -Theory

School of Mathematics, Yancheng Teachers University, Yancheng 224002, China

Received 13 October 2013; Accepted 8 February 2014; Published 9 April 2014

Academic Editor: Gualberto Solís-Perales

Copyright © 2014 Liping Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the problem of cluster anticonsensus of multiagent systems. For multiagent continuous systems, a new control protocol is designed based on the -theory. Then by LaSalle's invariance principle we prove that if the graph is connected and bipartite, then the cluster anticonsensus is achieved by the proposed control protocol. On the other hand, a similar control protocol is designed for multiagent discrete-time systems. Then, sufficient conditions are given to guarantee the cluster anticonsensus of multiagent discrete-time systems by using the -theory and LaSalle's invariance principle. Numerical simulations show the effectiveness of our theoretical results.