Vulnerability of dynamic systems

The purpose of this paper is to formulate and partially resolve the problem of vulnerability of dynamic systems in the context of the theory of directed graphs. A system is considered vulnerable if its structural properties such as input (output) reachability or structural controllability (observability) is destroyed by a perturbation characterized as removal of a line, or set of lines, from the corresponding graph. Graph-theoretic procedures are developed to identify the minimal sets of lines which are essential for preserving the structural properties of the system.