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 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(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 less than or equal to 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 converge 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.