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Discrete abstractions have become a standard approach to assist controlsynthesis under complex specifications. Most techniques for the construction ofdiscrete 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 thiswork, we aim at addressing this problem by considering only state-spaceabstraction. Firstly, we connect the continuous-time concrete system with itsdiscrete (state-space) abstraction with a control interface. Then, a novelstability notion called controlled globally asymptotic/practical stability withrespect to a set is proposed. It is shown that every system, under thecondition that there exists an admissible control interface such that theaugmented system (composed of the concrete system and its abstraction) can bemade controlled globally practically stable with respect to the given set, isapproximately simulated by its discrete abstraction. The effectiveness of theproposed results is illustrated by a simulation example.

Approximately symbolic models for a class of continuous-time nonlinear systems