The sampled-data boundary control problem for a longitudinal flexible bat i
s formulated as a linens discrete-time control problem in an infinite-dimen
sional state space. With zero-order-hold applied to the control channel, th
e system is lifted into an infinite sequence of constant control problems,
The finite-dimensional approximation of the discrete-time system is control
lable-observable if the sampling period satisfies some in-equality constrai
nts, which are related to the associated eigenvalues.