This paper presents controller design methods for dynamical systems that are observed by discrete sensors. These sensors induce a partitioning of the state space and only this quantized information is available for the controller. The so-called quantized system is modelled by a discrete-event model that serves as a basis for the controller design methods. However, instead of using solely the classical control methodologies for discrete-event systems as found in the literature, improvements are proposed by including additional information provided by the fact that the underlying plant is continuous by nature, such as continuity of the state trajectories and information on derivatives that holds for parts of the state space. The concept of discretely controlled invariant sets will play a crucial role in the development of control strategies and necessary and sufficient conditions for controlled invariance are presented. Also algorithms are included to compute the smallest and largest discretely controlled invariant sets with respect to a given set. All the techniques and computations are explicitly described by Boolean matrices and vectors and are ready for application. This is demonstrated for a benchmark problem of a two tank system.