Security Metrics for Uncertain Interconnected Systems under Stealthy Data Injection Attacks

This paper quantifies the security of uncertain interconnected systems under stealthy data injection attacks. In particular, we consider a large-scale system composed of a certain subsystem interconnected with an uncertain subsystem, where only the input-output channels are accessible. An adversary is assumed to inject false data to maximize the performance loss of the certain subsystem while remaining undetected. By abstracting the uncertain subsystem as a class of admissible systems satisfying an $\mathcal{L}_2$ gain constraint, the worst-case performance loss is obtained as the solution to a convex semi-definite program depending only on the certain subsystem dynamics and such an $\mathcal{L}_2$ gain constraint. This solution is proved to serve as an upper bound for the actual worst-case performance loss when the model of the entire system is fully certain. The results are demonstrated through numerical simulations of the power transmission grid spanning Sweden and Northern Denmark.