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

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/v10006-008-0025-8Search in Google Scholar

Cai, K. and Ishii, H. (2012). Average consensus on general strongly connected digraphs, Automatica 48(11): 2750-2761.10.1016/j.automatica.2012.08.003Search in Google Scholar

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.2004.834433Search in Google Scholar

Gantmacher, F.R. (1959). The Theory ofMatrices, Chelsea, New York, NY.Search in Google Scholar

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.2003.812781Search in Google Scholar

Khalil, H.K. (2002). Nonlinear Systems, Second Edition, Prentice Hall, Englewood Cliffs, NJ.Search in Google Scholar

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.Search in Google Scholar

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.2004.841888Search in Google Scholar

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.2006.887293Search in Google Scholar

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.2013.12.026Search in Google Scholar

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.2005.846556Search in Google Scholar

Shamma, J. (2008). Cooperative Control of Distributed Multi- Agent Systems, Wiley, New York, NY.10.1002/9780470724200Search in Google Scholar

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.75.122610060237Search in Google Scholar

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/v10006-009-0051-1Search in Google Scholar

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.2009.0658Search in Google Scholar