Topology-Independent Robust Stability of Homogeneous Dynamic Networks
Franco Blanchini, Daniele Casagrande, Giulia Maria Giordano, Umberto Viaro · IFAC-PapersOnLine · 2017
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 .