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Mathematical Problems in Engineering
Volume 2013, Article ID 192351, 13 pages
Research Article

State Consensus Analysis and Design for High-Order Discrete-Time Linear Multiagent Systems

1College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China
2College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China

Received 17 April 2013; Accepted 17 June 2013

Academic Editor: Guanghui Wen

Copyright © 2013 Yanrong Ge 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 paper deals with the state consensus problem of high-order discrete-time linear multiagent systems (DLMASs) with fixed information topologies. We consider three aspects of the consensus analysis and design problem: (1) the convergence criteria of global state consensus, (2) the calculation of the state consensus function, and (3) the determination of the weighted matrix and the feedback gain matrix in the consensus protocol. We solve the consensus problem by proposing a linear transformation to translate it into a partial stability problem. Based on the approach, we obtain necessary and sufficient criteria in terms of Schur stability of matrices and present an analytical expression of the state consensus function. We also propose a design process to determine the feedback gain matrix in the consensus protocol. Finally, we extend the state consensus to the formation control. The results are explained by several numerical examples.