  We present a scalable set-valued safety-preserving controller for constrained
continuous-time linear time-invariant (LTI) systems subject to additive,
unknown but bounded disturbance or uncertainty. The approach relies upon a
conservative approximation of the discriminating kernel using robust maximal
reachable sets---an extension of our earlier work on computation of the
viability kernel for high-dimensional systems. Based on ellipsoidal techniques
for reachability, a piecewise ellipsoidal algorithm with polynomial complexity
is described that under-approximates the discriminating kernel under LTI
dynamics. This precomputed piecewise ellipsoidal set is then used online to
synthesize a permissive state-feedback safety-preserving controller. The
controller is modeled as a hybrid automaton and can be formulated such that
under certain conditions the resulting control signal is continuous across its
transitions. We show the performance of the controller on a twelve-dimensional
flight envelope protection problem for a quadrotor with actuation saturation
and unknown wind disturbances.
