Positive Systems pp 91-99
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.
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- 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