Fault detection and isolation for systems defined over graphs

We consider the problem of fault detection and isolation for a class of linear dynamical systems defined by a graph containing faulty vertices and observer vertices. Using a geometric approach, we provide a characterization of the smallest conditioned invariant subspaces generated by faults in terms of the underlying graph structure. Based on this characterization, we give graph-theoretic conditions guaranteeing fault detectability. In addition, we provide a condition under which fault detectability fails.