  Discrete abstractions have become a standard approach to assist control
synthesis under complex specifications. Most techniques for the construction of
discrete abstractions are based on sampling of both the state and time spaces,
which may not be able to guarantee safety for continuous-time systems. In this
work, we aim at addressing this problem by considering only state-space
abstraction. Firstly, we connect the continuous-time concrete system with its
discrete (state-space) abstraction with a control interface. Then, a novel
stability notion called controlled globally asymptotic/practical stability with
respect to a set is proposed. It is shown that every system, under the
condition that there exists an admissible control interface such that the
augmented system (composed of the concrete system and its abstraction) can be
made controlled globally practically stable with respect to the given set, is
approximately simulated by its discrete abstraction. The effectiveness of the
proposed results is illustrated by a simulation example.
