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This paper provides a new analytic test to check strong accessibility of nonlinear control systems. This test can be applied to nonlinear systems described by meromorphic vector fields (whose components are fractions of analytic functions). The test consists in checking the rank of a certain finite matrix (which extends to a nonlinear case the classical “controllability matrix” of linear systems theory) and, unlike the classical accessibility test, always terminates giving an exhaustive answer (yes/no) within a fixed number of steps. Further, a generic feature of accessibility is proven: the accessibility from a point $p$ of the system analyticity domain implies the accessibility from almost every point of the domain (generic strong accessibility). The paper provides two simple examples, which illustrate the proposed analytic test and its advantages with respect to the existing results. [ABSTRACT FROM AUTHOR]

An algebraic framework for discrete-time nonlinear control systems is introduced, based on the forward and backward shifts of the vector fields. It appears to be the dual of the framework based on the differential 1-forms. As applications, the characterization of accessibility and the solution to the static state feedback linearization problem are stated in terms of the given vector fields. [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]