×

Relative flatness and flatness of implicit systems. (English) Zbl 1097.93019

Authors’ abstract: In this work we define the concept of relative flatness of a system with respect to a subsystem. The subsystem associated to a set of outputs of a system is constructed, and called here output subsystem. It is shown that the relative flatness of a system with respect to the output subsystem implies the flatness of the corresponding implicit system obtained by setting these outputs to zero. A sufficient condition of relative flatness based on a relative derived flag is presented. Based on these results, a sufficient condition for the flatness of a class of nonlinear implicit systems is obtained.
According to a correct remark made in the introduction the “approach is based on the infinite dimensional geometric setting” recently introduced in control theory” especially by the following paper: M. Fliess, J. Lévine, P. Martin and P. Rouchon [A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems, IEEE Trans. Autom. Control, 44, 922–937 (1999; Zbl 0964.93028)].

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93B18 Linearizations
93B29 Differential-geometric methods in systems theory (MSC2000)

Citations:

Zbl 0964.93028
PDFBibTeX XMLCite
Full Text: DOI