On reduced-order adaptive output error identification and adaptive IIR filtering

The reduced-order application of Landau's adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output (or desired signal in adaptive filter parlance). It is proven in this paper that if this perturbation signal is sufficiently small and a reduced-order dimension model is sufficiently excited, then the output and parameter estimates of this adaptive identifier/filter remain bounded. The influence of various operating conditions on this quantitatively defined bound are noted. This robustness property is crucial in all real applications, which due to nonlinearities and distributed effects are subject to reduced-order modeling.