Rational Basis Functions for Robust Identification from Frequency and Time-Domain Measurements

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 inH2.