Consensus of second-order multi-agent systems with time delays and slow switching topology

In this paper we investigate the problem of deriving sufficient conditions for asymptotic consensus of second-order multi-agent systems with slow switching topology and time delays. The proposed local interaction protocol is PD-like and the stability analysis is based on the Lyapunov-Krasovski functional method. Our approach is based on the computation of a set of parameters that guarantee stability under any network topology of a given set. A significant feature of this method is that it does not require to know the possible network topologies but only a bound on their second largest eigenvalue (algebraic connectivity). Note that this is only a preliminary work in this framework and the computation of the minimum dwell time that ensures asymptotic consensus under arbitrary switching is still an open issue and will be the object of our future research in this topic.