Perfect Attackability of Linear Dynamical Systems with Bounded Noise

This paper addresses the problem of secure state estimation in the presence of attacks on sensor measurements of a linear time invariant (LTI) system. We assume that the system is equipped with a common l
₀
-based attack-resilient state estimator and a sound anomaly detector. We introduce the notion of perfect attackability (PA) for LTI systems with bounded noise, when the attacker may introduce an unbounded estimation error while remaining undetected by the anomaly detector. Finally, necessary and sufficient conditions for perfectly attackable systems are provided, and illustrated on examples.