The paper addresses rigorous constraint satisfaction for linear continuous-time systems under piecewise constant control. To guarantee constraint satisfaction, we discretize the system and design adapted constraints in such a way that constraint satisfaction of the discretized system w.r.t. the adapted constraints implies constraint satisfaction of the continuous-time system w.r.t. the original constraints. Compared to existing approaches, the new method described in this paper is less conservative, not restricted to any specific control scheme (e.g., MPC), and computationally efficient.