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A canonical expansion for nonlinear systems. (English) Zbl 0618.93028
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

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
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