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 H1(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 Hp(Π), 1<p<∞. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in Hp(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 Hp(Π) and (D is the open unit disk) Hp(D), 1<p<∞. The results in this paper have application in system identification, model reduction, and control system synthesis.