On robust control algorithms for nonlinear network consensus protocols

Even though many consensus protocol algorithms have been developed over the last several years in the literature, robustness properties of these algorithms involving nonlinear dynamics have been largely ignored. Robustness here refers to sensitivity of the control algorithm achieving semistability and consensus in the face of model uncertainty. In this paper, we develop robust control algorithms for network consensus protocols with information model uncertainty of a specified structure. In particular, we construct homogeneous control protocol functions that scale in a consistent fashion with respect to a scaling operation on an underlying space with the additional property that the protocol functions can be written as a sum of functions, each homogeneous with respect to a fixed scaling operation, that retain system semistability and consensus.