Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential-Geometric Decomposition of Flat Nonlinear Discrete-Time
  Systems   We prove that every flat nonlinear discrete-time system can be decomposed by
coordinate transformations into a smaller-dimensional subsystem and an
endogenous dynamic feedback. For flat continuous-time systems, no comparable
result is available. The advantage of such a decomposition is that the complete
system is flat if and only if the subsystem is flat. Thus, by repeating the
decomposition at most $n-1$ times, where $n$ is the dimension of the state
space, the flatness of a discrete-time system can be checked in an algorithmic
way. If the system is flat, then the algorithm yields a flat output which only
depends on the state variables. Hence, every flat discrete-time system has a
flat output which does not depend on the inputs and their forward-shifts.
Again, no comparable result for flat continuous-time systems is available. The
algorithm requires in each decomposition step the construction of state- and
input transformations, which are obtained by straightening out certain vector
fields or distributions with the flow-box theorem or the Frobenius theorem.
Thus, from a computational point of view, only the calculation of flows and the
solution of algebraic equations is needed. We illustrate our results by two
examples.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci