In this paper, model sets for continuous--time linear time invariant
systems that are spanned by fixed pole orthonormal bases are
investigated. These bases generalise the well known Laguerre and
two--parameter Kautz cases. It is shown that the obtained model sets
are norm dense in the Hardy space $H_1(Pi)$ under the same
condition as previously derived by the authors for the norm
denseness in the ($Pi$ is the open right half plane) Hardy spaces
$H_p(Pi)$, $1 < p <infty$. As a further extension, the paper
shows how orthonormal model sets, that are norm dense in $H_p(Pi)$,
$1<p<infty$ and which have a prescribed asymptotic order may be
constructed. Finally, it is established that the Fourier series
formed by orthonormal basis functions converge in all spaces
$H_p(Pi)$, $1<p<infty$. The results in this paper have
application in system identification, model reduction and control
system synthesis.