A decentralized algorithm for assigning the weighting parameters in a general synchronous consensus network

We consider a network with the following goal: the state at each node of the network must iteratively converge to the same value; this value being some specified weighted average of the initial states of the network. To achieve this goal requires the construction of a matrix of weighting parameters with specific properties. In this paper, we present an iterative algorithm for determining these weighting parameters in a decentralized fashion; the weighting parameters are specified by the network nodes and each node only specifies the weighting parameters associated with that node. The results do not require that the communication graph of the network be bidirectional, but do require synchronous communication.