On Integrability of Observable Space for Discrete-Time Polynomial Control Systems

The goal of the technical note is to extend the results on the observability decomposition of continuous-time nonlinear systems into the discrete-time polynomial systems. In general, the observable space related to the concept of single-experiment observability of the discrete-time nonlinear systems cannot always be locally spanned by exact one-forms whose integrals would define the observable state coordinates. In this technical note, we show that for the special subclass of reversible polynomial systems, the observable space is integrable like in the continuous-time case.