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Mathematical Problems in Engineering
Volume 2013, Article ID 469747, 11 pages
Research Article

Swarm Stability Analysis of High-Order Linear Time-Invariant Singular Multiagent Systems

1Departemnt of Control Theory, College of Automation, Harbin Engineering University, Harbin 150001, China
2Departemnt of Control Theory, College of Automation, Northeastern University, Shenyang 110000, China

Received 5 May 2013; Revised 15 June 2013; Accepted 24 June 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 Mingyu Fu 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.


The swarm stability problem of high-order linear time-invariant (LTI) singular multiagent systems with directed graph topology is investigated extensively. Consensus of multiagent systems can be regarded as a specific case of swarm stability problem. Necessary and sufficient conditions for both swarm stability and consensus are presented. These conditions depend on the graph topology and generalized inverse theory, the dynamics of agents, and interaction among the neighbours. Several examples to illustrate the effectiveness of theoretical results are given.