Have a personal or library account? Click to login
A generalization of the graph Laplacian with application to a distributed consensus algorithm Cover

A generalization of the graph Laplacian with application to a distributed consensus algorithm

By: Guisheng Zhai  
Open Access
|Jun 2015

References

  1. Bauer, P.H. (2008). New challenges in dynamical systems: The networked case, International Journal of Applied Mathematics and Computer Science 18(3): 271-277, DOI: 10.2478/v10006-008-0025-8.10.2478/v10006-008-0025-8
  2. Cai, K. and Ishii, H. (2012). Average consensus on general strongly connected digraphs, Automatica 48(11): 2750-2761.10.1016/j.automatica.2012.08.003
  3. Fax, J.A. and Murray, R.M. (2004). Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control 49(9): 1465-1476.10.1109/TAC.2004.834433
  4. Gantmacher, F.R. (1959). The Theory ofMatrices, Chelsea, New York, NY.
  5. Jadbabaie, A., Lin, J. and Morse, A.S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control 48(6): 988-1001.10.1109/TAC.2003.812781
  6. Khalil, H.K. (2002). Nonlinear Systems, Second Edition, Prentice Hall, Englewood Cliffs, NJ.
  7. Mohar, B. (1991). The Laplacian spectrum of graphs, in Y. Alavi, G. Chartrand, O. Ollermann and A. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, NY.
  8. Moreau, L. (2005). Stability of multi-agent systems with time-dependent communication links, IEEE Transactions on Automatic Control 50(2): 169-182.10.1109/TAC.2004.841888
  9. Olfati-Saber, R., Fax, J.A. and Murray, R.M. (2007). Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95(1): 215-233.10.1109/JPROC.2006.887293
  10. Priolo, A., Gasparri, A., Montijano, E. and Sagues, C. (2014). A distributed algorithm for average consensus on strongly connected weighted digraphs, Automatica 50(3): 946-951.10.1016/j.automatica.2013.12.026
  11. Ren, W. and Beard, R.W. (2005). Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control 50(5): 655-661.10.1109/TAC.2005.846556
  12. Shamma, J. (2008). Cooperative Control of Distributed Multi- Agent Systems, Wiley, New York, NY.10.1002/9780470724200
  13. Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I. and Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles, Physical Review Letters 75(6): 1226-1229.10.1103/PhysRevLett.75.122610060237
  14. Zhai, G., Okuno, S., Imae, J. and Kobayashi, T. (2009). A matrix inequality based design method for consensus problems in multi-agent systems, International Journal of Applied Mathematics and Computer Science 19(4): 639-646, DOI: 10.2478/v10006-009-0051-1.10.2478/v10006-009-0051-1
  15. Zhai, G., Takeda, J., Imae, J. and Kobayashi, T. (2010). Towards consensus in networked nonholonomic systems, IET Control Theory & Applications 4(10): 2212-2218. 10.1049/iet-cta.2009.0658
DOI: https://doi.org/10.1515/amcs-2015-0027 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 353 - 360
Submitted on: Jan 6, 2014
Published on: Jun 25, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2015 Guisheng Zhai, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.