Convergence to Consensus by General Averaging
We investigate sufficient conditions for a discrete nonlinear non-homogeneous dynamical system to converge to consensus. We formulate a theorem which is based on the notion of averaging maps. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.
KeywordsConvex Hull Multiagent System General Average Opinion Dynamics Global Attractivity
Unable to display preview. Download preview PDF.
- 3.Hendrickx, J.M., Blondel, V.D.: Convergence of Different Linear and Non-Linear Vicsek Models. CESAME research report 2005.57 (2005)Google Scholar
- 5.Lorenz, D.A., Lorenz, J.: On conditions for convergence to consensus. arXiv.org/abs/0803.2211 (March 2008)Google Scholar
- 7.Lorenz, J.: Repeated Averaging and Bounded Confidence – Modeling, Analysis and Simulation of Continuous Opinion Dynamics. PhD thesis, Universität Bremen (March 2007)Google Scholar
- 8.Moreau, L.: Stability of Multiagent Systems with Time-Dependent Communication Links. IEEE Transactions on Automatic Control 50(2) (2005)Google Scholar
- 10.Wolfowitz, J.: Products of Indecomposable, Aperiodic, Stochastic Matrices. In: Proceedings of the American Mathematical Society Eugene, vol. 15, pp. 733–737 (1963)Google Scholar