  In this paper, we present how to synthesize controllers to enforce
$\omega$-regular properties over linear control systems affected by bounded
disturbances. In particular, these controllers are synthesized based on
so-called hybrid controlled invariant (HCI) sets. To compute these sets, we
first construct a product system between the linear control system and the
deterministic Streett automata (DSA) modeling the desired property. Then, we
compute the maximal HCI set over the state set of the product system by
leveraging a set-based approach. To ensure termination of the computation of
the HCI sets within a finite number of iterations, we also propose two
iterative schemes to compute approximations of the maximal HCI set. Finally, we
show the effectiveness of our results via two case studies.
