  For LTI control systems, we provide mathematical tools - in terms of Linear
Matrix Inequalities - for computing outer ellipsoidal bounds on the reachable
sets that attacks can induce in the system when they are subject to the
physical limits of the actuators. Next, for a given set of dangerous states,
states that (if reached) compromise the integrity or safe operation of the
system, we provide tools for designing new artificial limits on the actuators
(smaller than their physical bounds) such that the new ellipsoidal bounds (and
thus the new reachable sets) are as large as possible (in terms of volume)
while guaranteeing that the dangerous states are not reachable. This guarantees
that the new bounds cut as little as possible from the original reachable set
to minimize the loss of system performance. Computer simulations using a
platoon of vehicles are presented to illustrate the performance of our tools.
