Denition 6.1. We say that the system (\(X \times U \times\mathbb{R}_{\infty}^{m},\overline{f}\)) (resp. (\(X \times\mathbb{R}^{n}_{\infty}, \tau_{X}, F\))), with m inputs, is flat, or, shortly, flat, if and only if it is L-B equivalent to the trivial system (\(\mathbb{R}_{\infty}^{m}, \tau_{m}\)) (resp.(\(\mathbb{R}_{\infty}^{m}, \tau_{m},0\))), where \(\tau_{m}\) is the trivial Cartan field of \(\mathbb{R}_{\infty}^{m}\) with coordinates (\(y,$\textit{\.{y}}\textit{\"{y}},$\ldots\)):
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© 2009 Springer-Verlag Berlin Heidelberg
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Lévine, J. (2009). Differentially Flat Systems. In: Analysis and Control of Nonlinear Systems. Mathematical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00839-9_6
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DOI: https://doi.org/10.1007/978-3-642-00839-9_6
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