  The design of feedback control systems to block observability in a network
synchronization model, i.e. to make the dynamics unobservable from measurements
at a subset of the network's nodes, is studied. First, a general design
algorithm is presented for blocking observability at any specified group of $m$
nodes, by applying state feedback controls at $m+2$ specified actuation nodes.
The algorithm is based on a method for eigenstructure assignment, which allows
surgical modification of particular eigenvectors to block observability while
preserving the remaining open-loop eigenstructure. Next, the topological
structure of the network is exploited to reduce the number of controllers
required for blocking observability; the result is based on blocking
observability on the nodes associated with a vertex-cutset separating the
actuation and measurement locations. Also, the design is modified to encompass
regional feedback controls, which only use data from a subset of accessible
nodes. The regional feedback design does not maintain the open-loop
eigenstructure, but can be guaranteed to preserve stability via a time-scale
argument. The results are illustrated with numerical examples.
