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 S₁ obtained by the discretization of a linear time-invariant continuous-time system with a first-order hold. Equivalence of the reachability and controllability of S₁ is also shown. Similar results are given also for observability and reconstructibility. It turns out that S₁ is reachable only if S₀ is reachable, while S₁ is observable if and only if S₄l0 is observable, where S₀ is the sampled-data system obtained by the discretization with a zero-order hold of the same sampling period