Consensus algorithms are input-to-state stable

In many cooperative control problems, a shared knowledge of information provides the basis for cooperation. When this information is different for each agent, a state of noncooperation can result. Consensus algorithms ensure that after some time the agents would agree on the information critical for coordination, called the coordination variable. In this paper we show that if the coordination algorithm is input-to-state stable where the input is considered to be the discrepancy between the coordination variable known to each vehicle, then cooperation is guaranteed when a consensus scheme is used to synchronize information. A coordinated timing example is shown in simulation to illustrate the notions of stability when a coordination algorithm is augmented with a consensus strategy.