ARX modeling of unstable linear systems

TL;DR

This paper extends ARX modeling techniques to unstable linear systems, enabling accurate system and noise model identification even when unstable poles are not shared, which was a limitation of previous methods.

Contribution

It introduces modifications to ARX modeling that allow for the identification of unstable systems with non-shared unstable poles, broadening the applicability of ARX models.

Findings

Successfully generalizes ARX modeling for unstable systems

Enables accurate noise model retrieval with non-shared unstable poles

Improves system identification robustness for unstable plants

Abstract

High-order ARX models can be used to approximate a quite general class of linear systems in a parametric model structure, and well-established methods can then be used to retrieve the true plant and noise models from the ARX polynomials. However, this commonly used approach is only valid when the plant is stable or if the unstable poles are shared with the true noise model. In this contribution, we generalize this approach to allow the unstable poles not to be shared, by introducing modifications to correctly retrieve the noise model and noise variance.