Relative flatness and flatness of implicit systems

In this work we de ne the concept of relative flatness of a system with res pect to a subsystem. The subsystem associated to a set of outputs of a syst em is constructed, and called here output subsystem. It is shown that the r elative flatness of a system with respect to the output subsystem implies t he flatness of the corresponding implicit system obtained by setting these outputs to zero. A sufficient condition of relative flatness based on a rel ative derived ag is presented. Based on these results, a sufficient conditi on for the flatness of a class of nonlinear implicit systems is obtained.