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Multi-Group Consensus of Heterogeneous Fractional-Order Nonlinear Agents via Pinning Control

[+] Author Affiliations
Wei Sun

University of Science & Technology Beijing, Beijing, China

YangQuan Chen

Utah State University, Logan, UT

Changpin Li

Shanghai University, Shanghai, China

Paper No. DETC2011-48151, pp. 377-383; 7 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME


The present work concerns the multi-group consensus behavior of directed complex networks. The network consists of agents with heterogeneous fractional-order non-linear dynamics. It can be divided into several groups due to their dynamics or equilibriums. Each group will be stabilized at an equilibrium and different groups may have different steady state values. A necessary and sufficient condition is provided for the proposed pinning control law to be locally Mittag-Leffler stable. The conclusion turns to guarantee the exponential stable for integer-order systems. The collection of heterogeneous equilibriums is determined by the geometric multiplicity of the zero eigenvalue respect to the graph Laplacian. Simulations on fractional-order chaotic systems demonstrated the conclusions.

Copyright © 2011 by ASME



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