Using Feedback to Block Controllability at Remote Nodes in Network Synchronization Processes

The design of local state-feedback control systems to prevent controllability at remote network nodes is studied. An algorithm based on a joint eigenvalue-right eigenvector assignment method is developed, which under broad conditions maintains all the eigenvalues of the open-loop system while blocking controllability from selected remote nodes. Additionally, the graph structure of the network is exploited to enable controllability-blocking based on regional feedback, where only state measurements in a network partition are required. The design based on regional feedback does not preserve eigenvalue locations, however a modification of the design based on timescale separation is presented which guarantees stability. The results are illustrated with a numerical example.