Accessing the Role of Communication Link and Node Robustness in Interconnected Systems via Eigenvalue Sensitivity

Communication networks provide a larger flexibility for control design of large-scale interconnected systems by allowing the information exchange between local controllers of the subsystems and may improve the overall system performance. However, it is not well understood how significant the role of the communication link is in improving the system performance and how the network structure influences the robustness of the interconnected system. In this paper, we first demonstrate via a numerical simulation that certain communication links of the distributed control play important role in improving the overall system performance. Next, based on eigenvalue sensitivity analysis, we characterize those links explicitly for interconnection of scalar identical subsystems with ring and uniform extended star physical topologies. We further apply the method to investigate the relation between network robustness and the physical interconnection topology under some local perturbations. It is observed that there exists a trade-off between designing an interconnected system with high robustness and low communication cost for the considered topologies.