  We present a sound and automated approach to synthesize safe digital feedback
controllers for physical plants represented as linear, time invariant models.
Models are given as dynamical equations with inputs, evolving over a continuous
state space and accounting for errors due to the digitalization of signals by
the controller. Our approach has two stages, leveraging counterexample guided
inductive synthesis (CEGIS) and reachability analysis. CEGIS synthesizes a
static feedback controller that stabilizes the system under restrictions given
by the safety of the reach space. Safety is verified either via BMC or abstract
acceleration; if the verification step fails, we refine the controller by
generalizing the counterexample. We synthesize stable and safe controllers for
intricate physical plant models from the digital control literature.
