Geodesic
Relationship between discrete and continuous time systems
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 71-88 
A. Vagharshakyan. Relationship between discrete and continuous time systems. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 71-88. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a2/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The input and output signals of a continuous-time system can be registered only at fixed time moments, separated at least by a lap $h>0$. It is natural to ask whether the information obtained permits us to restore the original continuous-time system uniquely. Theoretically, it is possible to solve this problem, by letting $h>0$ tend to zero. However, the value of $h$ depends upon technical possibilities, and it is important to solve this problem for fixed values of $h>0$. In this paper we prove that it is possible to organize the passage to the discrete-time system lossless of information by a suitable choice of input continuous-time signals. It is desirable, of course, that the resulting discrete-time system have bounded transfer function. Here we give conditions on the continuous-time system that provide that property.

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