Orthonormal basis functions for continuous-time systems and Lp convergence

In this paper, model sets for linear-time invariant continuous-time 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 everywhere dense in the Hardy space H_1(#PI#) under the same condition as previously derived by the authors for the denseness in the (#PI# is the open right half plane) Hardy spaces H_p(#PI#), 1<p<#infinity#. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in H_p(#PI#), 1#<=#p<#infinity# and which have a prescribed asymptotic order may be constructed. Finally, it is established that the Fourier series formed by orthonormal basis functions coverge in all spaces H_p(#PI#) and (D is the open unit disk) H_p(D), 1<p<#infinity#. The results in this paper have application in system identification, model reduction and control system synthesis. (orig.)Available from TIB Hannover: RA 6154(440) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman