Consensus over multi-hop networked systems subject to heterogeneous time delays

Today great attention it has been posed on the consensus protocols that allow every agent automatically converge to a common consensus state using only local information received from its one hop neighboring agents. We consider the problem of reaching a consensus in multi-hop networked systems where each agent can access to the state of its m-hops neighboring agents. Additionally the presence of heterogeneous time delays affecting the communication through the multi-hop path is considered. Multi-hop and link time delay are unavoidable features of realistic networked system architectures based on wireless sensor networks. In this scenario, we derive condition to reach a consensus which is an explicit function of the system parameters including the delay bound, network topology, number of hop. Also a tradeoff between the convergence speed and the time delay is discussed.