Asymptotic Consensus Solutions in Non-Linear Delayed Distributed Algorithms Under Deterministic & Stochastic Perturbations

We consider a multi-agent non-linear delayed model which sustains consensus type of solutions. We use fixed point theory arguments to establish sufficient conditions for existence and uniqueness of solutions that converge exponentially fast to a common value with prescribed rate. The conditions depend on the communication topology, the nonlinearity of the model as well as the delay in the propagation of information. Furthermore we test the robustness of our results in the presence of independent time varying perturbations both deterministic and stochastic.