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Observability of nonlinear systems with unknown inputs was recently characterized in terms of dimension of an observability codistribution, obtained from Lie derivatives of outputs with respect to an infinite set of vector fields. However, the suggested stopping criterion does not apply to all systems, and the applicability condition is difficult to check. This article provides a new stopping criterion which holds universally and is easy to check. Moreover, we show that for systems with $n$ states, in the single-input single-output case the algorithm for computing observability codistribution converges in no more than $3n-1$ steps, while in the multi-input multi-output case addition of each independent input or output channel reduces this upper bound by one. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]