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A definition of a general type of sampling mechanism at the input and the output of a continuous-time system is given. The coefficients of the resulting discrete-time system are computed and conditions for controllability and stabilizability are derived. Also, the problem is considered whether the system can be made controllable by a suitable linear connection of the sampling mechanism and the continuous-time system. Finally, it is shown that if the continuous-time system is controllable and an arbitrary sampling time is given, then a sampling mechanism can be constructed such that the sampled system is controllable. Similar results are obtained with stabilizability instead of controllability.