This paper 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 \(\chi^2\) 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.

The code is written in Matlab R2009b (7.9.0.529).

• plotellipsoid.m
• position.m
• velocity.m