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Journal of Applied Mathematics
Volume 2012, Article ID 840873, 13 pages
Research Article

Distributed Containment Control of Networked Fractional-Order Systems with Delay-Dependent Communications

1College of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
2Key Laboratory of Autonomous Systems and Network Control, Ministry of Education, Guangzhou 510640, China
3School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798

Received 5 March 2012; Accepted 26 May 2012

Academic Editor: Baocang Ding

Copyright © 2012 Xueliang Liu 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.


This paper is concerned with a containment problem of networked fractional-order system with multiple leaders under a fixed directed interaction graph. Based on the neighbor rule, a distributed protocol is proposed in delayed communication channels. By employing the algebraic graph theory, matrix theory, Nyquist stability theorem, and frequency domain method, it is analytically proved that the whole follower agents will flock to the convex hull which is formed by the leaders. Furthermore, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is obtained. As a special case, the interconnection topology under the undirected case is also discussed. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.