Consensus problem of double-integrator dynamics system under time-varying networks

In this paper we study the consensus conditions for multi-agent systems under continuous time-varying network. The dynamics of agents is described by a double-integrator. For such multi-agent systems the connectivity of network is neither sufficient, nor necessary condition. Even if the integral connectivity condition given by [11], [12] is not sufficient condition of its consensus anymore. Under a general setting two sufficient conditions for consensus of the multi-agent system in time-varying network are provided. The first condition guarantees that the multi-agent system achieves consensus in an exponential rate. Under the second, a milder connectivity condition for network the multi-agent system achieves consensus, but it may be not in an exponential rate.