Rational basis functions for robust identification from frequency and time-domain measurements

Wed 11 Apr 2018 13:30:46 AEST

This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two--parameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown, that by using a min--max criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to re--parameterise the model structures into new ones with equivalent fixed poles, but for which the basis functions are orthonormal in H₂(D).

Orthonormal basis functions for continuous-time systems and Lp convergence

Wed 11 Apr 2018 12:15:33 AEST

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