Necessary and Sufficient Conditions for Difference Flatness

In this article, we show that the flatness of a nonlinear discrete-time system can be checked by computing unique sequence involutive distributions. The well-known test for static feedback linearizability is included as special case. Since computation distributions requires only solution algebraic equations, it allows an efficient implementation in computer algebra program. case positive result, flat output obtained straightening out with Frobenius theorem.