Preservation of controllability under sampling

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Abstract
In this paper we consider sampled-data systems realized by linear time-invariant continuous systems whose inputs are piecewise constant. The problem dealt with is the following : assuming that the continuous system is controllable, what are the necessary and sufficient conditions for the sampled-data system to be controllable ? We derive a necessary condition for the multidimensional case and show that a weaker condition than that required by Kalman et al. (1962) is needed for sufficiency.

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