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.