LTI Continuous Time Consensus Dynamics with Multiple and Distributed Delays
Christoforos Somarakis, John S. Baras
Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1495-1501, Platanias-Chania, Crete, Greece, June 25-28, 2013.
We study linear time invariant (LTI) continuous time consensus dynamics in the presence of bounded communication delays. Contrary to traditional Lyapunov based methods, we approach the problem using Fixed Point Theory. This method, allows us to create an appropriate complete functional metric space and through contraction mappings to establish the existence and uniqueness of a solution of this model. We explore the case of constant as well as distributed delays.