Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 273140, 21 pages
Research Article

Second-Order Consensus for Multiagent Systems under Directed and Switching Topologies

Institute of Intelligent Systems and Decision, Wenzhou University, Zhejiang 325027, China

Received 24 June 2011; Accepted 25 August 2011

Academic Editor: Zidong Wang

Copyright © 2012 Lixin Gao 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 consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double-integrator model. Two different cases are considered: one is the leader-following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor-based feedback laws in both leader-following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.