Preservation of reachability and observability under sampling with a first-order hold

This paper gives the necessary and sufficient condition for the reachability of the sampled-data system S/sub 1/ obtained by the discretization of a linear time-invariant continuous-time system with a first-order hold. Equivalence of the reachability and controllability of S/sub 1/ is also shown. Similar results are given also for observability and reconstructibility. It turns out that S/sub 1/ is reachable only if S/sub 0/ is reachable, while S/sub 1/ is observable if and only if S/sub 4/l0 is observable, where S/sub 0/ is the sampled-data system obtained by the discretization with a zero-order hold of the same sampling period.<
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