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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]

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]

This paper focuses on computational aspects of the realization of nonlinear multi-input multi-output systems. Instead of the algorithmic solutions, provided in earlier works, the explicit formulas are presented, which enable to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The solution is based on the concept of adjoint polynomials and requires a minimal amount of computations. The formulas are implemented in computer algebra system Mathematica and made available online via web Mathematica tools. [ABSTRACT FROM PUBLISHER]

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]