Abstract
In this paper, model sets for linear-time-invariant continuous-time systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalize the well-known Laguerre and two-parameter Kautz cases. It is shown that the obtained model sets are everywhere dense in the Hardy space H 1(Π) under the same condition as previously derived by the authors for the denseness in the (Π is the open right half plane) Hardy spaces H p(Π), 1<p<∞. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in H p(Π), 1≤p<∞, 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(Π) and (D is the open unit disk) H p(D), 1<p<∞. The results in this paper have application in system identification, model reduction, and control system synthesis.
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