For given system dynamics, control structure, and fault/attack detection procedure, we provide mathematical tools–in terms of Linear Matrix Inequalities (LMIs)–for characterizing and minimizing the set of states that sensor attacks can induce in the system while keeping the alarm rate of the fault detector sufficiently close to its false alarm rate in the attack-free case. This quantifies the attack's potential impact when it is constrained to stay hidden from the detector. Simulation results are presented to illustrate the performance of our tools.@en