Performance degradation of stealthy attacks against sensor measurements in vector systems

In this work, we analyze the performance degradation of stealthy attacks against sensor measurements in vector systems. Two types of attacks are considered. One is strictly stealthy attack and the other is ϵ-stealthy attack. For the strictly stealthy attack, we characterize the upper bound of the performance degradation and design an optimal strictly stealthy attack that can achieve the upper bound. For the ϵ-stealthy attack, we quantify the upper bound of the performance degradation and propose a sub-optimal ϵ-stealthy attack approximately achieving the upper bound. Numerical results are given to illustrate the trade off between performance degradation versus the stealthiness level of the attack.