Distributed agreement in the presence of noise

In this paper, we propose a distributed dynamic consensus scheme which exhibits noise resilient property. In our setup, each node is modeled as a simple integrator. We use frequency-domain analysis to establish that the output of each node tracks the (weighted) average of the inputs of all nodes with zero steady-state error and show that a certain kind of graph Laplacain (called feasible Laplacian) is necessary in our framework. The eigenvalue location of feasible Laplacians turns out to be an LMI region, which allows us to derive an LMI test condition. When the noise is present, we show that the output tracking error has a bounded covariance.