Pereira da Silva, Paulo Sérgio; Corrêa Filho, Carlos Relative flatness and flatness of implicit systems. (English) Zbl 1097.93019 SIAM J. Control Optimization 39, No. 6, 1929-1951 (2001). 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)]. Reviewer: Peter Kraut (Erlabrunn) Cited in 9 Documents MSC: 93C15 Control/observation systems governed by ordinary differential equations 93B18 Linearizations 93B29 Differential-geometric methods in systems theory (MSC2000) Keywords:flatness; relative flatness; nonlinear systems Citations:Zbl 0964.93028 PDFBibTeX XMLCite \textit{P. S. Pereira da Silva} and \textit{C. Corrêa Filho}, SIAM J. Control Optim. 39, No. 6, 1929--1951 (2001; Zbl 1097.93019) Full Text: DOI