Novel Vulnerability Metrics for Interdependent System based on System Controllability

Abstract

In this paper we develop novel vulnerability metrics for interdependent critical infrastructures or economic sectors based on the concept of controllability. Specifically, we consider the Input-Output Inoperability Model, that represents the dynamics of the dependencies and interdependencies among infrastructures or sectors during an adverse event or malicious attack, and we argue that the more the system is controllable via an external perturbation that represents the fault or attack, the more the system is vulnerable. Therefore, we analyze the vulnerability of the system in terms of the magnitude of the associated controllability matrix. Moreover, based on the proposed index, we develop a simple defensive strategy to reduce the effect of an attack. A validation of the approach with respect to real data concludes the paper.