Control-channel interactions in diffusive dynamical networks: A graph-theoretic perspective

Control-channel interactions in a linear diffusive network model are studied, with the aim of determining the role of the network's topology in such interactions. Specifically, the influence of a built controller on the infinite and finite zero structure of a second control channel is characterized. The analysis shows how the network's graph topology, the relative positions of the two channels, and the architecture of the built controller influence the zero structure of the second control channel. Further, the influence of low or high gain controller designs on remote channels is examined. The analyses demonstrate that some control architectures and positions can introduce undesirable nonminimum-phase dynamics at remote locations, while others are guaranteed to maintain or promote minimum-phase dynamics.