Topology-Independent Robust Stability of Homogeneous Dynamic Networks

The paper presents conditions for the stability of a dynamical network described by a directed graph, whose nodes represent dynamical systems characterised by the same transfer function F(s) and whose edges account for the interactions between pairs of nodes. In turn, these interactions depend via a transference G(s) on the outputs of the subsystems associated with the connected nodes. The stability conditions are topology-independent, in that they hold for all possible connections of the nodes, and robust, in that they allow for uncertainties in the determination of the transferences. Two types of interactions are considered: bidirectional and unidirectional. In the first case, if nodes i and j are connected, both node i affects node j and node j affects node i, while in the second case only one of the two occurrences is admitted. The robust stability conditions are expressed as constraints for the Nyquist diagram of H = FG.