Passivity results for information dissemination in sensor networks

We derive the largest possible class of linear time-invariant controllers, M^RS, to synthesize the information dissemination policies that ensure the closed-loop stability for resource constrained sensor networks. We assume that the sensory information is routed using a tree-topology. Our main contribution is the use of the Zames-Falb multipliers to preserve positivity of repeating monotone nonlinearities that are encountered in a noncooperative game theoretic optimization problem. We show that M^RS fails to ensure the closed-loop incremental stability in general but does ensure it for the special case wherein the setpoints are allowed to vary with time at either only the parent or only the children.