This paper analyzes the effect of replay attacks on a control system. We assume an attacker wishes to disrupt the operation of a control system in steady state. In order to inject an exogenous control input without being detected the attacker will hijack the sensors, observe and record their readings for a certain amount of time and repeat them afterwards while carrying out his attack. This is a very common and natural attack (we have seen numerous times intruders recording and replaying security videos while performing their attack undisturbed) for an attacker who does not know the dynamics of the system but is aware of the fact that the system itself is expected to be in steady state for the duration of the attack. We assume the control system to be a discrete time linear time invariant gaussian system applying an infinite horizon Linear Quadratic Gaussian (LQG) controller. We also assume that the system is equipped with a X~2 failure detector. The main contributions of the paper, beyond the novelty of the problem formulation, consist in 1) providing conditions on the feasibility of the replay attack on the aforementioned system and 2) proposing a countermeasure that guarantees a desired probability of detection (with a fixed false alarm rate) by trading off either detection delay or LQG performance, either by decreasing control accuracy or increasing control effort.
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