Scalable Metrics to Quantify Security of Large-scale Systems

This paper addresses the issue of data injection attacks on the actuators of positive networked control systems. We introduce an impact metric that quantifies the worst-case performance loss caused by stealthy attacks. By leveraging the properties of positive systems, we show that the impact metric admits an equivalent linear program representation, offering scalability advantages. Under mild assumptions, we prove the existence of a solution for the linear program, thereby proving that the impact metric admits a finite value. Furthermore, we extend such scalable metrics for uncertain systems and provide brief insights into cone positive systems.