  Sampled-data (SD) systems, which are composed of both discrete- and
continuous-time components, are arguably one of the most common classes of
cyberphysical systems in practice; most modern controllers are implemented on
digital platforms while the plant dynamics that are being controlled evolve
continuously in time. As with all cyberphysical systems, ensuring hard
constraint satisfaction is key in the safe operation of SD systems. A powerful
analytical tool for guaranteeing such constraint satisfaction is the viability
kernel: the set of all initial conditions for which a safety-preserving control
law (that is, a control law that satisfies all input and state constraints)
exists. In this paper we present a novel sampling-based algorithm that tightly
approximates the viability kernel for high-dimensional sampled-data linear
time-invariant (LTI) systems. Unlike prior work in this area, our algorithm
formally handles both the discrete and continuous characteristics of SD
systems. We prove the correctness and convergence of our approximation
technique, provide discussions on heuristic methods to optimally bias the
sampling process, and demonstrate the results on a twelve-dimensional flight
envelope protection problem.
