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Abstract
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.
Notes
† The research reported herein was supported by the U.S. Department of Energy, under Contract DE-AC03-77ET29138.