On the Performance Degradation of Cyber-Physical Systems Under Stealthy Integrity Attacks

This technical note analyzes the effect of stealthy integrity attacks on Cyber-Physical Systems, which is modeled as a Stochastic Linear Time-Invariant (LTI) system equipped with a linear filter, a linear feedback controller and a χ 2 failure detector. An attacker wishes to induce perturbation in the control loop by compromising a subset of the sensors and injecting an exogenous control input, without incurring detection from an anomaly detector. We show how the problem can be modeled, from the attacker's standpoint, as a constrained control problem and that the characterization of the maximum perturbation can be posed as reachable set computation, which we solve using ellipsoidal calculus.