Link-failure detection in network synchronization processes

We study the detection of link failures in network synchronization processes. In particular, for a canonical linear network synchronization model, we consider detection of a critical link's failure by a monitor that makes noisy local measurements of the process. We characterize Maximum A-Posteriori (MAP) detection of the link failure, for both the case that the monitor has information about the network's initial state and the random-initial-condition case. Several algebraic, spectral and graph theoretic characterizations of the detector and its performance are provided. These include conditions under which the link failure is completely hidden from the monitor and, conversely, conditions that permit perfect detection with sufficient data. Our analyses highlight that rather effective detection is possible with limited and noisy observation data.