Orthonormal basis functions for continuous-time systems: Completeness and Lp-convergence

Abstract

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 Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H_p(Π), 1 ≤ p <; ∞ and the right half plane algebra A(Π) provided that a mild condition on the choice of basis poles is satisfied. As a further extension, the paper shows how orthonormal model sets, that are norm dense in A_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 A_p(Π), 1 ≤ p <; ∞. The results in this paper have application in system identification, model reduction and control system synthesis.