Topology-dependent stability of a network of dynamical systems with communication delays

In this paper, we analyze the stability of a network of first-order linear time-invariant systems with constant, identical communication delays. We investigate the influence of both system parameters and network characteristics on stability. In particular, a non-conservative stability bound for the delay is given such that the network is asymptotically stable for any delay smaller than this bound. We show how the network topology changes the stability bound. Exemplarily, we use these results to answer the question if a symmetric or skew-symmetric interconnection is preferable for a given set of subsystems.