  We present a convex optimization to reduce the impact of sensor falsification
attacks in linear time invariant systems controlled by observer-based feedback.
We accomplish this by finding optimal observer and controller gain matrices
that minimize the size of the reachable set of attack-induced states. To avoid
trivial solutions, we integrate a covariance-based $\|H\|_2$ closed-loop
performance constraint, for which we develop a novel linearization for this
typically nonlinear, non-convex problem. We demonstrate the effectiveness of
this linear matrix inequality framework through a numerical case study.
