Su, Renjeng; Hunt, L. R. A canonical expansion for nonlinear systems. (English) Zbl 0618.93028 IEEE Trans. Autom. Control 31, 670-673 (1986). In the first part of the paper the authors consider n vector fields \(X_ 1,...,X_ n\) which are linear independent and analytic in a neighborhood of the origin of \({\mathbb{R}}^ n\). A local coordinate system based on \(X_ 1,...,X_ n\) is constructed, and it is shown that in this coordinate system each analytic vector field has a series expansion whose coefficients are computed in terms of Lie brackets. In the second part, the authors apply this result to control systems of the form \[ \dot x=f(x)+\sum^{m}_{i=1}g_ i(x)u_ i \] which satisfy suitable assumptions. The resulting expansion allows us to find out the feedback linearizable part of the given system. Reviewer: A.Bacciotti Cited in 12 Documents MSC: 93C10 Nonlinear systems in control theory 57R27 Controllability of vector fields on \(C^\infty\) and real-analytic manifolds 93B27 Geometric methods 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 93C15 Control/observation systems governed by ordinary differential equations Keywords:vector fields; series expansion; Lie brackets PDF BibTeX XML Cite \textit{R. Su} and \textit{L. R. Hunt}, IEEE Trans. Autom. Control 31, 670--673 (1986; Zbl 0618.93028) Full Text: DOI