ARX modeling of unstable linear systems
It extends a standard system identification approach to a broader class of systems, addressing a known limitation for unstable plants.
The paper generalizes ARX modeling to handle unstable linear systems where unstable poles are not shared with the noise model, enabling correct retrieval of the noise model and variance.
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.